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A NOTE ON UPPER AND LOWER SOLUTIONS METHOD FOR FOURTH-ORDER BOUNDARY VALUE PROBLEMS
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作者 Zhao Hong (School of Math.,Changchun Normal University,Changchun 130032) 《Annals of Differential Equations》 2008年第1期117-120,共4页
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
关键词 fourth-order boundary value problem EXISTENCE upper and lower solution method
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EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS
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作者 Du Zengji Lin Xiaojie Ge Weigao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2005年第3期323-330,共8页
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
关键词 vector differential equation nonlinear boundary value problem existence and uniqueness upper and lower solutions method.
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ASYMPTOTIC BEHMIOUR IN A REACTION-DIFFUSION SYSTEM
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作者 黄淑祥 谢春红 《Acta Mathematica Scientia》 SCIE CSCD 1998年第1期57-62,共6页
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.
关键词 Semilinear parabolic systems asymptotic behavior upper and lower solutions method Lp-estimate duality technique semigroup theorem
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A Class of Singularly Perturbed Boundary Value Problems Arising from Catalytic Reactions
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作者 史少云 《Northeastern Mathematical Journal》 CSCD 2000年第3期367-372,共6页
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
关键词 Singularly perturbed boundary value problem nonexponentially decayed boundary layer upper and lower solutions method
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Existence and Uniqueness of Positive Solutions for Some Singular Boundary Value Problems with Linear Functional Boundary Conditions 被引量:2
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作者 Zeng Qin ZHAO Fu Shan LI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第10期2073-2084,共12页
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
关键词 Linear functional boundary condition decreasing function positive solution upper and lower solution method fixed point theorem
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BOUNDARY VALUE PROBLEM FOR NON-LINEAR SECOND ORDER ORDINARY DIFFERENTIAL EQUATION WITH DISCONTINUOUS TERMS IN BANACH SPACE
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作者 Jin'e Shi Guozhong Cui 《Analysis in Theory and Applications》 2009年第4期349-354,共6页
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.
关键词 method of upper and lower solutions decreasing operator fixed point mono-tone operator
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A NUMERICAL METHOD FOR SOLVING NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF FREDHOLM TYPE
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作者 Igor Boglaev 《Journal of Computational Mathematics》 SCIE CSCD 2016年第3期262-284,共23页
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
关键词 Nonlinear integro-parabolic equations of Fredholm type Nonlinear differenceschemes Monotone iterative methods The method of upper and lower solutions.
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BOUNDARY VALUE PROBLEM FOR FIRST ORDER IMPULSIVE DIFFERENTIAL EQUATION WITH A PARAMETER AND INFINITE DELAY
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作者 Du Binbin Shi Bao (Institute of Applied Math., Naval Aeronautical Engineering Institute, Yantai 264001) 《Annals of Differential Equations》 2006年第3期261-265,共5页
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
关键词 IMPULSIVE infinite delay the method of upper and lower solutions
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