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
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
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.
A class of singularly perturbed boundary value problems arising from the catalytic reactions in chemical engineering is observed. That kind of p roblems exhibits the behavior of nonexponentially decayed boundary la...A class of singularly perturbed boundary value problems arising from the catalytic reactions in chemical engineering is observed. That kind of p roblems exhibits the behavior of nonexponentially decayed boundary layer, and he nce the study of asymptotic behavior of their solutions seems more diffcult. The uniformly valid asymptotic expansions of solutions as well as their derivatives are given via the upper and lower solutions method, and those estimates seem qu ite accurate.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
By using upper and lower solutions and fixed point theorem we give the existence theorem of non-linear second order ordinary differential equation with discontinuous terms in Banach Space.
The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterativ...The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterative method yields two sequences which converge monotonically from above and below, respectively, to a solution of a nonlinear difference scheme. This monotone convergence leads to an existence-uniqueness theorem. An analy- sis of convergence rates of the monotone iterative method is given. Some basic techniques for construction of initial upper and lower solutions are given, and numerical experiments with two test problems are presented.展开更多
In this paper, we consider a boundary problem of first order impulsive differential equation with a parameter and infinite delay. By using the method of upper and lower solutions, we get some sufficient conditions for...In this paper, we consider a boundary problem of first order impulsive differential equation with a parameter and infinite delay. By using the method of upper and lower solutions, we get some sufficient conditions for the existence of its solutions.展开更多
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.
文摘A class of singularly perturbed boundary value problems arising from the catalytic reactions in chemical engineering is observed. That kind of p roblems exhibits the behavior of nonexponentially decayed boundary layer, and he nce the study of asymptotic behavior of their solutions seems more diffcult. The uniformly valid asymptotic expansions of solutions as well as their derivatives are given via the upper and lower solutions method, and those estimates seem qu ite accurate.
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By using upper and lower solutions and fixed point theorem we give the existence theorem of non-linear second order ordinary differential equation with discontinuous terms in Banach Space.
文摘The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterative method yields two sequences which converge monotonically from above and below, respectively, to a solution of a nonlinear difference scheme. This monotone convergence leads to an existence-uniqueness theorem. An analy- sis of convergence rates of the monotone iterative method is given. Some basic techniques for construction of initial upper and lower solutions are given, and numerical experiments with two test problems are presented.
基金Research supported by Distinguished Expert Science Foundation of Naval Aeronautical Engineering Institute.
文摘In this paper, we consider a boundary problem of first order impulsive differential equation with a parameter and infinite delay. By using the method of upper and lower solutions, we get some sufficient conditions for the existence of its solutions.
