Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we pro...Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.展开更多
In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equ...In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.展开更多
In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We ...In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We prove that (1) possesses at most one limit cycle and give out the necessary and sufficient conditions of existence and uniqueness of limit cycles.展开更多
In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These co...In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.展开更多
Although the isogeometric collocation(IGA-C)method has been successfully utilized in practical applications due to its simplicity and efficiency,only a little theoretical results have been established on the numerical...Although the isogeometric collocation(IGA-C)method has been successfully utilized in practical applications due to its simplicity and efficiency,only a little theoretical results have been established on the numerical analysis of the IGA-C method.In this paper,we deduce the convergence rate of the consistency of the IGA-C method.Moreover,based on the formula of the convergence rate,the necessary and sufficient condition for the consistency of the IGA-C method is developed.These results advance the numerical analysis of the IGA-C method.展开更多
In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also ex...In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also extended and improved in this paper.展开更多
Clarifying the necessary conditions for the emergence of payments for ecosystem services (PES) and the situational variables that affect PES is the basis for their interpretation, prediction, and selection. This artic...Clarifying the necessary conditions for the emergence of payments for ecosystem services (PES) and the situational variables that affect PES is the basis for their interpretation, prediction, and selection. This article proposes an analytical framework for the emergence of PES and argues that the key to determining whether PES can occur and whether a selected PES program is appropriate is to evaluate the net gain. When payers anticipate that a PES program will provide a satisfactory number of ES and a net gain over the opportunity cost and will cover all costs, it is assumed that the program will be implemented. When it is difficult to accurately evaluate the net gain of PES, the situational variables that affect the costs and benefits need to be examined. The group characteristics, ES characteristics, spatial and temporal contacts between the suppliers and demanders, correlation with private goods and additionality are important situational variables that affect the emergence and choice of PES.展开更多
This paper deals with the existence of positive solutions for the singular fourth order boundary value problem.A necessary and sufficient condition for the existence of C3 positive solution is given by means of the mo...This paper deals with the existence of positive solutions for the singular fourth order boundary value problem.A necessary and sufficient condition for the existence of C3 positive solution is given by means of the monotone iterative technique.Furthermore,the uniqueness of the C3 positive solution,and the iterative sequence of the C3 positive solution are also obtained.展开更多
In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of ne...In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.展开更多
In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v,...In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v, nonincreasing on v for each x,u; there exists a constant q∈(0,1) such that t qf(x,t -1 u,tu)f(x,u,u)λ qf(x,λ -1 u,λu),0<t<1<λ, u∈R +. Then a necessary and sufficient condition for the equation u″+f(x,u,u)=0 on the boundary condition αu(a)-βu′(a)=0, γ(b)+δu′(b)=0 to have C 1(I) nonzero solutions is that 0<∫ b af(x,e(x),e(x))dx<∞, where α,β,γ,δ are nonnegative real numbers, Δ=(b-a)αγ+αδ+βγ>0, e(x)=G(x,x), G(x,y) is Green's function of above mentioned boundary value problem (when f(x,u,v)≡0). Received September 9,1996. Revised March 31,1997. 1991 MR Subject Classification: 34B.展开更多
In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the mult...In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a (weakly) LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.展开更多
This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump diffusions.The controlled system is described by a stochastic differential systems driven by Poisson random measur...In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump diffusions.The controlled system is described by a stochastic differential systems driven by Poisson random measure and an independent Brownian motion.The control domain is assumed to be convex.Pointwise second-order maximum principle for controlled jump diffusion in terms of the martingale with respect to the time variable is proved.The proof of the main result is based on variational approach using the stochastic calculus of jump diffusions and some estimates on the state processes.展开更多
In order to study the mechanism of confined water inrush from coal seam floor,the main influences on permeability in the process of triaxial seepage experiments were analyzed with methods such as laboratory experiment...In order to study the mechanism of confined water inrush from coal seam floor,the main influences on permeability in the process of triaxial seepage experiments were analyzed with methods such as laboratory experiments,theoretical analysis and mechanical model calculation.The crack extension rule and the ultimate destruction form of the rock specimens were obtained.The mechanism of water inrush was explained reasonably from mechanical point of view.The practical criterion of water inrush was put forward.The results show that the rock permeability "mutation" phenomenon reflects the differences of stress state and cracks extension rate when the rock internal crack begins to extend in large-scale.The rock ultimate destruction form is related to the rock lithology and the angle between crack and principal stress.The necessary condition of floor water inrush is that the mining pressure leads to the extension and transfixion of the crack.The sufficient condition of floor water inrush is that the confined water’s expansionary stress in normal direction and shear stress in tangential direction must be larger than the internal stress in the crack.With the two conditions satisfied at the same time,the floor water inrush accident will occur.展开更多
To illustrate the general properties of the Beltrami flows,a new sufficient and necessary condi- tion of the general solution of the Beltrami flows has been given,on whose basis some sufficient and necessary condition...To illustrate the general properties of the Beltrami flows,a new sufficient and necessary condi- tion of the general solution of the Beltrami flows has been given,on whose basis some sufficient and necessary conditions and sufficient conditions in literature are unified.The advantages of the new expressions are that one may get solutions of Beltrami flows with constant proportional factors which satisfy some given asymptotic decaying conditions at infinity.Finally,we find a class of spherical vortices of Beltrami flows,where the mo- tion trajectories of the fluid particles are confined within a sphere or two adjacent concentric spherical shells.We find that the superpositions of the spherical vortices of the same order with different polar axes may produce chaotic trajectories.展开更多
The boundedness and the norm of a class of integral operators Ta,b,c on Lλ^P spaces are studied in this paper. The author not only gives the sufficient and necessary condition for the boundedness of Ta,b,c on Lλ^P,b...The boundedness and the norm of a class of integral operators Ta,b,c on Lλ^P spaces are studied in this paper. The author not only gives the sufficient and necessary condition for the boundedness of Ta,b,c on Lλ^P,but also obtains its accurate norm on Lλ^P for some range under the condition of c = n + a + b.展开更多
This paper derives necessary and sufficient conditions of optimality in the form of a stochastic maximum principle for relaxed and strict optimal control problems with jumps.These problems are governed by multi-dimens...This paper derives necessary and sufficient conditions of optimality in the form of a stochastic maximum principle for relaxed and strict optimal control problems with jumps.These problems are governed by multi-dimensional forward-backward doubly stochastic differential equations(FBDSDEs)with Poisson jumps and has firstly relaxed controls,which are measure-valued processes,and secondly,as an application,the authors allow them to have strict controls.The FBDSDEs with jumps are fully-coupled,the forward and backward equations work in different Euclidean spaces in general,the backward equation is Markovian,and the control problems are considered under full information or partial information in terms ofσ-algebras that provide such information.The formulation of these equations as well as performance functionals are given in abstract forms to allow the possibility to cover most of the applications available in the literature.Moreover,coefficients of such equations are allowed to depend on control variables.展开更多
The Kuhn-Tucker type necessary conditions of weak efficiency are given for the problem of mini- mizing a vector function whose each component is the sum of a differentiable function and a convex function, subjcct to a...The Kuhn-Tucker type necessary conditions of weak efficiency are given for the problem of mini- mizing a vector function whose each component is the sum of a differentiable function and a convex function, subjcct to a set of differentiable nonlinear inequalities on a convex subset C of R^n, under the conditions similar to the Abadie constraint qualification, or the Kuhn-Tucker constraint qualification, or the Arrow-Hurwicz-Uzawa constraint qualification.展开更多
This paper proposes a new chaotic system and its fractional-order chaotic system. The necessary condition for the existence of chaotic attractors in this new fractional-order system is obtained. It finds that this new...This paper proposes a new chaotic system and its fractional-order chaotic system. The necessary condition for the existence of chaotic attractors in this new fractional-order system is obtained. It finds that this new fractional-order system is chaotic for q 〉 0.783 if the system parameter m=6. The chaotic attractors for q=0.8, and q=0.9 are obtained. A circuit is designed to realize its fractional-order chaos system for q=0.9 by electronic workbench.展开更多
Consider the following equationwhere 6, c and τ are constants, and τ > 0, bc ≠ 0. In this paper, we establish a necessary and sufficient condition for zero solution of Eq.(*) to be asymptotically stable, which i...Consider the following equationwhere 6, c and τ are constants, and τ > 0, bc ≠ 0. In this paper, we establish a necessary and sufficient condition for zero solution of Eq.(*) to be asymptotically stable, which is easy to verify and apply.展开更多
基金supported by the Beijing Natural Science Foundation(1212003)。
文摘Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.
基金supported by an NSERC granta startup fund of University of Albertasupported by the NSF grant DMS1613163
文摘In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.
文摘In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We prove that (1) possesses at most one limit cycle and give out the necessary and sufficient conditions of existence and uniqueness of limit cycles.
文摘In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.
基金supported by the National Natural Science Foundation of China(61872316)the Natural Science Foundation of Zhejiang Province,China(LY19F020004)
文摘Although the isogeometric collocation(IGA-C)method has been successfully utilized in practical applications due to its simplicity and efficiency,only a little theoretical results have been established on the numerical analysis of the IGA-C method.In this paper,we deduce the convergence rate of the consistency of the IGA-C method.Moreover,based on the formula of the convergence rate,the necessary and sufficient condition for the consistency of the IGA-C method is developed.These results advance the numerical analysis of the IGA-C method.
文摘In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also extended and improved in this paper.
文摘Clarifying the necessary conditions for the emergence of payments for ecosystem services (PES) and the situational variables that affect PES is the basis for their interpretation, prediction, and selection. This article proposes an analytical framework for the emergence of PES and argues that the key to determining whether PES can occur and whether a selected PES program is appropriate is to evaluate the net gain. When payers anticipate that a PES program will provide a satisfactory number of ES and a net gain over the opportunity cost and will cover all costs, it is assumed that the program will be implemented. When it is difficult to accurately evaluate the net gain of PES, the situational variables that affect the costs and benefits need to be examined. The group characteristics, ES characteristics, spatial and temporal contacts between the suppliers and demanders, correlation with private goods and additionality are important situational variables that affect the emergence and choice of PES.
文摘This paper deals with the existence of positive solutions for the singular fourth order boundary value problem.A necessary and sufficient condition for the existence of C3 positive solution is given by means of the monotone iterative technique.Furthermore,the uniqueness of the C3 positive solution,and the iterative sequence of the C3 positive solution are also obtained.
基金Projects Supported by the Science Fund of the Chinese Academy of Sciences
文摘In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.
文摘In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v, nonincreasing on v for each x,u; there exists a constant q∈(0,1) such that t qf(x,t -1 u,tu)f(x,u,u)λ qf(x,λ -1 u,λu),0<t<1<λ, u∈R +. Then a necessary and sufficient condition for the equation u″+f(x,u,u)=0 on the boundary condition αu(a)-βu′(a)=0, γ(b)+δu′(b)=0 to have C 1(I) nonzero solutions is that 0<∫ b af(x,e(x),e(x))dx<∞, where α,β,γ,δ are nonnegative real numbers, Δ=(b-a)αγ+αδ+βγ>0, e(x)=G(x,x), G(x,y) is Green's function of above mentioned boundary value problem (when f(x,u,v)≡0). Received September 9,1996. Revised March 31,1997. 1991 MR Subject Classification: 34B.
文摘In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a (weakly) LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.
基金This work was supported by National Natural Science Foundation of China (10401041)Natural Science Foundation of Hubei Province (2004ABA009)
文摘This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
文摘In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump diffusions.The controlled system is described by a stochastic differential systems driven by Poisson random measure and an independent Brownian motion.The control domain is assumed to be convex.Pointwise second-order maximum principle for controlled jump diffusion in terms of the martingale with respect to the time variable is proved.The proof of the main result is based on variational approach using the stochastic calculus of jump diffusions and some estimates on the state processes.
基金supported by the Youth Innovation Fund of China(KJ-2013-TDKC-15)the Fostering and Doctor Startup Initial Fund Program of Xi’an University of Science and Technology(201350,2014QDJ033).
文摘In order to study the mechanism of confined water inrush from coal seam floor,the main influences on permeability in the process of triaxial seepage experiments were analyzed with methods such as laboratory experiments,theoretical analysis and mechanical model calculation.The crack extension rule and the ultimate destruction form of the rock specimens were obtained.The mechanism of water inrush was explained reasonably from mechanical point of view.The practical criterion of water inrush was put forward.The results show that the rock permeability "mutation" phenomenon reflects the differences of stress state and cracks extension rate when the rock internal crack begins to extend in large-scale.The rock ultimate destruction form is related to the rock lithology and the angle between crack and principal stress.The necessary condition of floor water inrush is that the mining pressure leads to the extension and transfixion of the crack.The sufficient condition of floor water inrush is that the confined water’s expansionary stress in normal direction and shear stress in tangential direction must be larger than the internal stress in the crack.With the two conditions satisfied at the same time,the floor water inrush accident will occur.
基金The project is supported by the National Foundamental Research Programme of State Commission of Sciences and Technology.
文摘To illustrate the general properties of the Beltrami flows,a new sufficient and necessary condi- tion of the general solution of the Beltrami flows has been given,on whose basis some sufficient and necessary conditions and sufficient conditions in literature are unified.The advantages of the new expressions are that one may get solutions of Beltrami flows with constant proportional factors which satisfy some given asymptotic decaying conditions at infinity.Finally,we find a class of spherical vortices of Beltrami flows,where the mo- tion trajectories of the fluid particles are confined within a sphere or two adjacent concentric spherical shells.We find that the superpositions of the spherical vortices of the same order with different polar axes may produce chaotic trajectories.
基金Supported by the National Natural Science Foundation of China(1142610411271124+5 种基金1120114111301136and 61473332)Natural Science Foundation of Zhejiang province(LQ13A010005LY15A010014)Teachers Project of Huzhou University(RP21028)
文摘The boundedness and the norm of a class of integral operators Ta,b,c on Lλ^P spaces are studied in this paper. The author not only gives the sufficient and necessary condition for the boundedness of Ta,b,c on Lλ^P,but also obtains its accurate norm on Lλ^P for some range under the condition of c = n + a + b.
基金Qassim University,represented by the Deanship of Scientific Research under Grant No.SR-D-015-3352the Algerian PRFU under Grant No.C00L03UN07120180005。
文摘This paper derives necessary and sufficient conditions of optimality in the form of a stochastic maximum principle for relaxed and strict optimal control problems with jumps.These problems are governed by multi-dimensional forward-backward doubly stochastic differential equations(FBDSDEs)with Poisson jumps and has firstly relaxed controls,which are measure-valued processes,and secondly,as an application,the authors allow them to have strict controls.The FBDSDEs with jumps are fully-coupled,the forward and backward equations work in different Euclidean spaces in general,the backward equation is Markovian,and the control problems are considered under full information or partial information in terms ofσ-algebras that provide such information.The formulation of these equations as well as performance functionals are given in abstract forms to allow the possibility to cover most of the applications available in the literature.Moreover,coefficients of such equations are allowed to depend on control variables.
基金Supported by the National Natural Science Foundation of China(No.70671064,No.60673177)the Province Natural Science Foundation of Zhejiang(No.Y7080184)the Education Department Foundation of Zhejiang Province(No.20070306)
文摘The Kuhn-Tucker type necessary conditions of weak efficiency are given for the problem of mini- mizing a vector function whose each component is the sum of a differentiable function and a convex function, subjcct to a set of differentiable nonlinear inequalities on a convex subset C of R^n, under the conditions similar to the Abadie constraint qualification, or the Kuhn-Tucker constraint qualification, or the Arrow-Hurwicz-Uzawa constraint qualification.
基金supported by Chongqing Education Committee of China (Grant No KJ070502)
文摘This paper proposes a new chaotic system and its fractional-order chaotic system. The necessary condition for the existence of chaotic attractors in this new fractional-order system is obtained. It finds that this new fractional-order system is chaotic for q 〉 0.783 if the system parameter m=6. The chaotic attractors for q=0.8, and q=0.9 are obtained. A circuit is designed to realize its fractional-order chaos system for q=0.9 by electronic workbench.
基金The work is supported by Natural Science Foundation of Heilongjiang Province of China, A0207.
文摘Consider the following equationwhere 6, c and τ are constants, and τ > 0, bc ≠ 0. In this paper, we establish a necessary and sufficient condition for zero solution of Eq.(*) to be asymptotically stable, which is easy to verify and apply.