In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one soluti...In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one solution for the problem. As an application, these results are applied to PBVP of ODE and some examples are given to illustrate our results.展开更多
A new upper and lower solution theory is presented for the second order problem (G'(y))'+ f(t, y) = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative,...A new upper and lower solution theory is presented for the second order problem (G'(y))'+ f(t, y) = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.展开更多
This paper is concerned with a third-order nonlinear separated boundary value problem. By the Leray-Schauder degree theory and the method of upper and lower solutions, we obtain the existence of at least three solutio...This paper is concerned with a third-order nonlinear separated boundary value problem. By the Leray-Schauder degree theory and the method of upper and lower solutions, we obtain the existence of at least three solutions to the problem.展开更多
In this paper,we deal with a class of boundary value problem.We give the existence of solution under the assumption that there exist lower and upper solutions to the problem.Our result extends and complements the rele...In this paper,we deal with a class of boundary value problem.We give the existence of solution under the assumption that there exist lower and upper solutions to the problem.Our result extends and complements the relevant ones which were obtained by many authors previously.展开更多
In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and perio...In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β展开更多
In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower soluti...In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.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 purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding ste...The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding steady state solutions. Then, the above results are extended to a semilinear parabolic equation with nonlinear boundary condition by analyzing the corresponding eigenvalue problem and using the method of upper and lower solutions.展开更多
This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme...This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.展开更多
The singularly perturbed initial value problem for a nonlinear singular equation is considered. By using a simple and special method the asymptotic behavior of solution is studied.
This paper is concerned with the following second-order vector boundary value problem :x^R=f(t,Sx,x,x'),0〈t〈1,x(0)=A,g(x(1),x'(1))=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,exis...This paper is concerned with the following second-order vector boundary value problem :x^R=f(t,Sx,x,x'),0〈t〈1,x(0)=A,g(x(1),x'(1))=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method.展开更多
In this paper, by the method of upper and lower solutions, we establish the existence of the non-trivial nonnegative periodic solutions for a class of degenerate diffusion system arising from dynamics of biological gr...In this paper, by the method of upper and lower solutions, we establish the existence of the non-trivial nonnegative periodic solutions for a class of degenerate diffusion system arising from dynamics of biological groups.展开更多
This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem a...This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.展开更多
In this paper, we obtain the existence and uniqueness of solutions for nonlinear boundary value problem s of the form v″= f(l,v,v′,T′v,T1v,T2v), v(0) = A, g(v(1),v'(1)) = 0with Volterra and Hammerstein operator...In this paper, we obtain the existence and uniqueness of solutions for nonlinear boundary value problem s of the form v″= f(l,v,v′,T′v,T1v,T2v), v(0) = A, g(v(1),v'(1)) = 0with Volterra and Hammerstein operators, by means of upper and lower solutions method.展开更多
By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f(t, u) ...By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f(t, u) is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0, 1] positive solutions as well as the C1 [0, 1] positive solutions.展开更多
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solution...Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.展开更多
In this paper,a fractional Laplacian mutualistic system under Neumann boundary conditions is studied.Using the method of upper and lower solutions,it is proven that the solutions of the fractional Laplacian strong mut...In this paper,a fractional Laplacian mutualistic system under Neumann boundary conditions is studied.Using the method of upper and lower solutions,it is proven that the solutions of the fractional Laplacian strong mutualistic model with Neumann boundary conditions will blow up when the intrinsic growth rates of species are large.展开更多
This paper proves the asymptotic behaviour for a class of reaction-diffusionsystem in bacteriology by using duality technique, semigroup theorem, Lp--estimates andupper and lower solutions method.
In this paper nonlinear boundary value problems for discontinuous delayed differen- tial equations are considered. Some existence and boundedness results of solutions are obtained via the method of upper and lower sol...In this paper nonlinear boundary value problems for discontinuous delayed differen- tial equations are considered. Some existence and boundedness results of solutions are obtained via the method of upper and lower solutions, which may be discontinuous. Our analysis can be applied to those phenomena from physics and control theory which have been successfully described by delayed differential equations with discontinuous functions, such as electric, pneu- matic, and hydraulic networks. It is also an important step to precede the design of control signals when finite-time or practical stability control are concerned.展开更多
TFD ( Thomas-Fermi-Dirac) equation in quantum mechanics is established. The existence theorems of the solutions are obtained by singular boundary value problem theory of ordinary differential equation and upper and lo...TFD ( Thomas-Fermi-Dirac) equation in quantum mechanics is established. The existence theorems of the solutions are obtained by singular boundary value problem theory of ordinary differential equation and upper and lower solution method.展开更多
文摘In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one solution for the problem. As an application, these results are applied to PBVP of ODE and some examples are given to illustrate our results.
基金Supported by Grant No.201/01/1451 of the Grant Agency of Czech Republicthe Council of Czech Government J14/98:153100011
文摘A new upper and lower solution theory is presented for the second order problem (G'(y))'+ f(t, y) = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.
基金supported by the National Natural Science Foundation of China (11071205)the NSF of Jiangsu Province (BK2008119)+1 种基金the NSF of the Education Department of Jiangsu Provincethe Innovation Project of Jiangsu Province Postgraduate Project
文摘This paper is concerned with a third-order nonlinear separated boundary value problem. By the Leray-Schauder degree theory and the method of upper and lower solutions, we obtain the existence of at least three solutions to the problem.
基金The work was supported by NNSF of China (No.10571021).
文摘In this paper,we deal with a class of boundary value problem.We give the existence of solution under the assumption that there exist lower and upper solutions to the problem.Our result extends and complements the relevant ones which were obtained by many authors previously.
文摘In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β
文摘In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.
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.
基金The project is supported by National Natural Science Foundation of China (10071026)
文摘The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding steady state solutions. Then, the above results are extended to a semilinear parabolic equation with nonlinear boundary condition by analyzing the corresponding eigenvalue problem and using the method of upper and lower solutions.
基金Supported by the Natural Science Foundation of China (11171120)the Doctoral Program of Higher Education of China (20094407110001)Natural Science Foundation of Guangdong Province (10151063101000003)
文摘This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.
基金Supported by Important Project of the National Natural Science Foundation of China( 90 2 1 1 0 0 4 ) andby the"Hundred Talents Project" of Chinese Academy of Science
文摘The singularly perturbed initial value problem for a nonlinear singular equation is considered. By using a simple and special method the asymptotic behavior of solution is studied.
文摘This paper is concerned with the following second-order vector boundary value problem :x^R=f(t,Sx,x,x'),0〈t〈1,x(0)=A,g(x(1),x'(1))=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method.
文摘In this paper, by the method of upper and lower solutions, we establish the existence of the non-trivial nonnegative periodic solutions for a class of degenerate diffusion system arising from dynamics of biological groups.
文摘This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.
文摘In this paper, we obtain the existence and uniqueness of solutions for nonlinear boundary value problem s of the form v″= f(l,v,v′,T′v,T1v,T2v), v(0) = A, g(v(1),v'(1)) = 0with Volterra and Hammerstein operators, by means of upper and lower solutions method.
基金. Supported by National Natural Science Foundation of China (Grant No. 10871116), Natural Science Foundation of Shandong Province of China (Grant No. ZR2010AM005) and the Doctoral Program Foundation of Education Ministry of China (Grant No. 200804460001)Acknowledgements The authors would like to thank the referees for their valuable comments.
文摘By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f(t, u) is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0, 1] positive solutions as well as the C1 [0, 1] positive solutions.
文摘Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.
基金partially supported by National Natural Science Foundation of China(11771380)Natural Science Foundation of Jiangsu Province(BK20191436).
文摘In this paper,a fractional Laplacian mutualistic system under Neumann boundary conditions is studied.Using the method of upper and lower solutions,it is proven that the solutions of the fractional Laplacian strong mutualistic model with Neumann boundary conditions will blow up when the intrinsic growth rates of species are large.
文摘This paper proves the asymptotic behaviour for a class of reaction-diffusionsystem in bacteriology by using duality technique, semigroup theorem, Lp--estimates andupper and lower solutions method.
基金Supported by the National Natural Science Foundation of China(Grants No.70703016 and No.10001024)Research Grant of the Business School of Nanjing University
文摘In this paper nonlinear boundary value problems for discontinuous delayed differen- tial equations are considered. Some existence and boundedness results of solutions are obtained via the method of upper and lower solutions, which may be discontinuous. Our analysis can be applied to those phenomena from physics and control theory which have been successfully described by delayed differential equations with discontinuous functions, such as electric, pneu- matic, and hydraulic networks. It is also an important step to precede the design of control signals when finite-time or practical stability control are concerned.
文摘TFD ( Thomas-Fermi-Dirac) equation in quantum mechanics is established. The existence theorems of the solutions are obtained by singular boundary value problem theory of ordinary differential equation and upper and lower solution method.