This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-e...The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-earthquake observations indicate that the displacement near the fault zone is typically nonuniform,and the fault plane position is uncertain.In this study,we first established a series of improved governing equations to analyze the mechanical response of tunnels under strike-slip fault dislocation.The proposed methodology incorporated key factors such as nonuniform fault displacement and uncertain fault plane position into the governing equations,thereby significantly enhancing the applicability range and accuracy of the model.In contrast to previous analytical models,the maximum computational error has decreased from 57.1%to 1.1%.Subsequently,we conducted a rigorous validation of the proposed methodology by undertaking a comparative analysis with a 3D finite element numerical model,and the results from both approaches exhibited a high degree of qualitative and quantitative agreement with a maximum error of 9.9%.Finally,the proposed methodology was utilized to perform a parametric analysis to explore the effects of various parameters,such as fault displacement,fault zone width,fault zone strength,the ratio of maximum fault displacement of the hanging wall to the footwall,and fault plane position,on the response of tunnels subjected to strike-slip fault dislocation.The findings indicate a progressive increase in the peak internal forces of the tunnel with the rise in fault displacement and fault zone strength.Conversely,an augmentation in fault zone width is found to contribute to a decrease in the peak internal forces.For example,for a fault zone width of 10 m,the peak values of bending moment,shear force,and axial force are approximately 46.9%,102.4%,and 28.7% higher,respectively,compared to those observed for a fault zone width of 50 m.Furthermore,the position of the peak internal forces is influenced by variations in the ratio of maximum fault displacement of the hanging wall to footwall and the fault plane location,while the peak values of shear force and axial force always align with the fault plane.The maximum peak internal forces are observed when the footwall exclusively bears the entirety of the fault displacement,corresponding to a ratio of 0:1.The peak values of bending moment,shear force,and axial force for the ratio of 0:1 amount to approximately 123.8%,148.6%,and 111.1% of those for the ratio of 0.5:0.5,respectively.展开更多
In this paper, we study the Schrodinger equations (-△)^(s)u + V(x)u = a(x)|u|^(p-2)u + b(x)|u|^(q-2)u, x∈R^(N),where 0 < s < 1, 2 < q < p < 2_(s)^(*), 2_(s)^(*) is the fractional Sobolev critical expo...In this paper, we study the Schrodinger equations (-△)^(s)u + V(x)u = a(x)|u|^(p-2)u + b(x)|u|^(q-2)u, x∈R^(N),where 0 < s < 1, 2 < q < p < 2_(s)^(*), 2_(s)^(*) is the fractional Sobolev critical exponent. Under suitable assumptions on V, a and b for which there may be no ground state solution, the existence of positive solutions are obtained via variational methods.展开更多
This paper discusses the necessary and sufficient conditions for the existence of Hermite positive definite solutions of the quaternion matrix equation X<sup>m</sup>+ B*XB = C (m > 0) and its iterative ...This paper discusses the necessary and sufficient conditions for the existence of Hermite positive definite solutions of the quaternion matrix equation X<sup>m</sup>+ B*XB = C (m > 0) and its iterative solution method. According to the characteristics of the coefficient matrix, a corresponding algebraic equation system is ingeniously constructed, and by discussing the equation system’s solvability, the matrix equation’s existence interval is obtained. Based on the characteristics of the coefficient matrix, some necessary and sufficient conditions for the existence of Hermitian positive definite solutions of the matrix equation are derived. Then, the upper and lower bounds of the positive actual solutions are estimated by using matrix inequalities. Four iteration formats are constructed according to the given conditions and existence intervals, and their convergence is proven. The selection method for the initial matrix is also provided. Finally, using the complexification operator of quaternion matrices, an equivalent iteration on the complex field is established to solve the equation in the Matlab environment. Two numerical examples are used to test the effectiveness and feasibility of the given method. .展开更多
Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of ...Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.展开更多
This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2...This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.展开更多
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(...By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].展开更多
In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the a...In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the application of the main theorem, two examples are given.展开更多
By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam w...By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.展开更多
A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. B...A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.展开更多
This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems ...This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.展开更多
We classify all positive solutions for the following integral system:{ui(x)=∫Rn1/│x-y│^n-α fi(u(y))dy,x∈R^n,i=1,…,m,0〈α〈n,and u(x)=(u1(x),u2(x)…,um(x)).Here fi(u), 1 ≤ i ≤m, monotone non...We classify all positive solutions for the following integral system:{ui(x)=∫Rn1/│x-y│^n-α fi(u(y))dy,x∈R^n,i=1,…,m,0〈α〈n,and u(x)=(u1(x),u2(x)…,um(x)).Here fi(u), 1 ≤ i ≤m, monotone nondecreasing are real-valued functions of homogeneous degree n+α/n-α and are monotone nondecreasing with respect to all the independent variables U1, u2, ..., urn.In the special case n ≥ 3 and α = 2. we show that the above system is equivalent to thefollowing elliptic PDE system:This system is closely related to the stationary SchrSdinger system with critical exponents for Bose-Einstein condensate展开更多
By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations wit...By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions.The results in this paper improve some known results.展开更多
In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions ...In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions are obtained.展开更多
This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian:{(φ(u′))′+a(t)f(u(t))=0, 0〈t〈1, αφ(u(...This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian:{(φ(u′))′+a(t)f(u(t))=0, 0〈t〈1, αφ(u(0))-βφ(u′(ξ))=0,γφ(u(1))+δφ(u′(η))0,where φ(x) = |x|^p-2x,p 〉 1, a(t) may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple (at least three) positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.展开更多
In this paper, the nonexistence of positive entire solutions for div(|Du| p-2 Du)q(x)f(u),x∈R N, is established, where p】1,Du=(D 1u,...,D Nu),q∶R N→(0,∞) and f∶(0,∞)→(0,∞) are continuous fun...In this paper, the nonexistence of positive entire solutions for div(|Du| p-2 Du)q(x)f(u),x∈R N, is established, where p】1,Du=(D 1u,...,D Nu),q∶R N→(0,∞) and f∶(0,∞)→(0,∞) are continuous functions.展开更多
In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D~α_(o^+)is the standard Riemann-Liouville fra...In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D~α_(o^+)is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel'skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.展开更多
In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term witho...In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.展开更多
The solvability of one dimensional fourth-order p-Laplace equations of the type [GRAPHICS] where, g(v) \ v \ (p-2) v, p > 1 is investigated. With cone compression/extension theorem, some existence and multiplicity ...The solvability of one dimensional fourth-order p-Laplace equations of the type [GRAPHICS] where, g(v) \ v \ (p-2) v, p > 1 is investigated. With cone compression/extension theorem, some existence and multiplicity results of positive solution have been required according to different growth condition of nonlinear form f at zero and at infinity.展开更多
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
基金Projects(52378411,52208404)supported by the National Natural Science Foundation of China。
文摘The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-earthquake observations indicate that the displacement near the fault zone is typically nonuniform,and the fault plane position is uncertain.In this study,we first established a series of improved governing equations to analyze the mechanical response of tunnels under strike-slip fault dislocation.The proposed methodology incorporated key factors such as nonuniform fault displacement and uncertain fault plane position into the governing equations,thereby significantly enhancing the applicability range and accuracy of the model.In contrast to previous analytical models,the maximum computational error has decreased from 57.1%to 1.1%.Subsequently,we conducted a rigorous validation of the proposed methodology by undertaking a comparative analysis with a 3D finite element numerical model,and the results from both approaches exhibited a high degree of qualitative and quantitative agreement with a maximum error of 9.9%.Finally,the proposed methodology was utilized to perform a parametric analysis to explore the effects of various parameters,such as fault displacement,fault zone width,fault zone strength,the ratio of maximum fault displacement of the hanging wall to the footwall,and fault plane position,on the response of tunnels subjected to strike-slip fault dislocation.The findings indicate a progressive increase in the peak internal forces of the tunnel with the rise in fault displacement and fault zone strength.Conversely,an augmentation in fault zone width is found to contribute to a decrease in the peak internal forces.For example,for a fault zone width of 10 m,the peak values of bending moment,shear force,and axial force are approximately 46.9%,102.4%,and 28.7% higher,respectively,compared to those observed for a fault zone width of 50 m.Furthermore,the position of the peak internal forces is influenced by variations in the ratio of maximum fault displacement of the hanging wall to footwall and the fault plane location,while the peak values of shear force and axial force always align with the fault plane.The maximum peak internal forces are observed when the footwall exclusively bears the entirety of the fault displacement,corresponding to a ratio of 0:1.The peak values of bending moment,shear force,and axial force for the ratio of 0:1 amount to approximately 123.8%,148.6%,and 111.1% of those for the ratio of 0.5:0.5,respectively.
基金supported by the NNSF of China(12171014, 12271539, 12171326)the Beijing Municipal Commission of Education (KZ202010028048)the Research Foundation for Advanced Talents of Beijing Technology and Business University (19008022326)。
文摘In this paper, we study the Schrodinger equations (-△)^(s)u + V(x)u = a(x)|u|^(p-2)u + b(x)|u|^(q-2)u, x∈R^(N),where 0 < s < 1, 2 < q < p < 2_(s)^(*), 2_(s)^(*) is the fractional Sobolev critical exponent. Under suitable assumptions on V, a and b for which there may be no ground state solution, the existence of positive solutions are obtained via variational methods.
文摘This paper discusses the necessary and sufficient conditions for the existence of Hermite positive definite solutions of the quaternion matrix equation X<sup>m</sup>+ B*XB = C (m > 0) and its iterative solution method. According to the characteristics of the coefficient matrix, a corresponding algebraic equation system is ingeniously constructed, and by discussing the equation system’s solvability, the matrix equation’s existence interval is obtained. Based on the characteristics of the coefficient matrix, some necessary and sufficient conditions for the existence of Hermitian positive definite solutions of the matrix equation are derived. Then, the upper and lower bounds of the positive actual solutions are estimated by using matrix inequalities. Four iteration formats are constructed according to the given conditions and existence intervals, and their convergence is proven. The selection method for the initial matrix is also provided. Finally, using the complexification operator of quaternion matrices, an equivalent iteration on the complex field is established to solve the equation in the Matlab environment. Two numerical examples are used to test the effectiveness and feasibility of the given method. .
文摘Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.
文摘This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.
基金National Natural Science Foundation of China( 198710 0 5 )
文摘By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].
基金The project supported by NNSF of China(10071080)
文摘In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the application of the main theorem, two examples are given.
文摘By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.
基金Supported by the National Natural Science Foundation of China (10961017)"Qinglan" Talent Programof Lanzhou Jiaotong University (QL-05-20A)
文摘A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.
基金The research supported by the National Natural Science Foundation of China.
文摘This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.
基金supported by NSF Grant DMS-0604638Li partially supported by NSF Grant DMS-0401174
文摘We classify all positive solutions for the following integral system:{ui(x)=∫Rn1/│x-y│^n-α fi(u(y))dy,x∈R^n,i=1,…,m,0〈α〈n,and u(x)=(u1(x),u2(x)…,um(x)).Here fi(u), 1 ≤ i ≤m, monotone nondecreasing are real-valued functions of homogeneous degree n+α/n-α and are monotone nondecreasing with respect to all the independent variables U1, u2, ..., urn.In the special case n ≥ 3 and α = 2. we show that the above system is equivalent to thefollowing elliptic PDE system:This system is closely related to the stationary SchrSdinger system with critical exponents for Bose-Einstein condensate
基金SuppoSed by the NSF of Anhui Provincial Education Depaxtment(KJ2012A265,KJ2012B187)
文摘By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions.The results in this paper improve some known results.
文摘In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions are obtained.
基金Tutorial Scientific Research Program Foundation of Education Department of Gansu Province(0710-04).
文摘This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian:{(φ(u′))′+a(t)f(u(t))=0, 0〈t〈1, αφ(u(0))-βφ(u′(ξ))=0,γφ(u(1))+δφ(u′(η))0,where φ(x) = |x|^p-2x,p 〉 1, a(t) may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple (at least three) positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.
文摘In this paper, the nonexistence of positive entire solutions for div(|Du| p-2 Du)q(x)f(u),x∈R N, is established, where p】1,Du=(D 1u,...,D Nu),q∶R N→(0,∞) and f∶(0,∞)→(0,∞) are continuous functions.
基金Supported by the Research Fund for the Doctoral Program of High Education of China(20094407110001)Supported by the NSF of Guangdong Province(10151063101000003)
文摘In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D~α_(o^+)is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel'skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.
基金supported by Science and Technology Project of Chongqing Municipal Education Committee (kJ110501) of ChinaNatural Science Foundation Project of CQ CSTC (cstc2012jjA20016) of ChinaNational Natural Science Foundation of China (11101298)
文摘In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.
文摘The solvability of one dimensional fourth-order p-Laplace equations of the type [GRAPHICS] where, g(v) \ v \ (p-2) v, p > 1 is investigated. With cone compression/extension theorem, some existence and multiplicity results of positive solution have been required according to different growth condition of nonlinear form f at zero and at infinity.