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Acta Mathematica Sinica,English Series 2007年第8期23卷 1447-1456页

作者： Bao Qiang YAN Donal O'REGAN Ravi P. AGARWAL Department of Mathematics Shandong Normal University Ji'nan 250014 P. R. China Department of Mathematics National University of Ireland Galway Ireland Department of Mathematical Science Florida Institute of Technology Melbourne FL32901 USA

This paper presents a lower and upper solution technique for singular second order boundary value problems on the half line.

关键词： boundary value problems lower and upper solutions Schauder＇s fixed point theorem

A class of singular perturbation solutions to semilinear equations of fourth order

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Applied Mathematics and Mechanics(English Edition) 2009年第11期30卷 1455-1460页

作者：莫嘉琪 Department of Mathematics Anhui Normal University Division of Computational Science E-Institute of Shanghai Universities at SJTU

A class of singularly perturbed boundary value problems for semilinear equations of fourth order with two parameters are considered. Under suitable conditions, using the method of lower and upper solutions, the existence and the asymptotic behavior of the solution to the boundary value problem are studied, In the present paper, the solution to the original singularly perturbed problem with two parameters has only one boundary layer.

关键词： nonlinear two parameters singular perturbation lower and upper solutions

Convergence of Monotone Iterations for Differential Problem

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Acta Mathematica Sinica,English Series 2000年第4期16卷 711-720页

作者： Tadeusz Jankowski Department of Differential Equations. Technical University of Gdansk 11/12 G. Narutowicz Str. 80 952 Gdansk. Poland

We use the method of lower and upper solutions combined with monotone iterations to differential problems with a parameter. Existence of extremal solutions to such problems is proved.

关键词： lower and upper solutions Monotone sequences Convergence Minimal and maximal solutions

Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations

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Acta Mathematica Sinica,English Series 2007年第12期23卷 2205-2212页

作者： Juan J.NIETO RosanaRODRGUEZ-LPEZ Departamento de Análisis Matemático Facultad de MatemáticasUniversidad de Santiago de Compostela

We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing mappings as well as non monotone mappings. We also present some applications to first-order ordinary differential equations with periodic boundary conditions, proving the existence of a unique solution admitting the existence of a lower solution.

关键词： fixed point partially ordered set first-order differential equation lower and upper solutions

EXTREME solutions OF INITIAL VALUE PROBLEMS FOR NONLINEAR SECOND ORDER INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES

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Acta Mathematicae Applicatae Sinica 2001年第3期17卷 289-295页

作者：陈芳启 Department of Mathematics Tianjin University Tianjin China Department of Mathematics Shandong University Jinan China

In this paper, using the monotone iterative method, we study the existence of extreme solutions of initial value problems for nonlinear second order integrodifferential equations in Banach spaces. Some existence theor... 详细信息

关键词： Iategrodifferential equations Kuratowski measure of noncompactness lower and upper solutions monotone iterative method

Existence of solutions to the Higher Order Nonlinear Differential Equations

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Chinese Quarterly Journal of Mathematics 2012年第1期27卷 1-10页

作者： TANG Lin-shan JIANG Cheng-shun Southwest Electronics and Telecommunication Technology Research Institute Chengdu 610041China Institute of Information and Computation Science Wuhan College of Zhongnan University of Econimics and LawWuhan 430079China

This paper is concerned with the following n-th ordinary differential equation:{u～(n)(t)=f(t,u(t),u～(1)(t),···,u～(n-1) (t)),for t∈(0,1),u～(i) (0)=0,0 ≤i≤n3,au～(n-2)(0)du～(n-1)(0)=0,cu～(n-2)(1)+du～(n-1)(1)=0,where a,c ∈ R,,≥,such that a～2 + b～2 >0 and c～2+d～2>0,n ≥ 2,f:[0,1] × R → R is a continuous function.Assume that f satisfies one-sided Nagumo condition,the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory,lower and upper solutions,a priori estimate technique.

关键词： n-th order boundary value problems one-sided Nagumo condition lower and upper solutions a priori estimates Leray-Schauder degree

PBVP of Integrodifferential Equations with Carathéodory Functions

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Acta Mathematica Sinica,English Series 1998年第4期14卷 463-472页

作者： Zhuang Wan Chen Yubo, Department of Mathematics, Shandong Normal University, Jinan 250014, China 山东师范大学数学系山东济南

We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.

关键词： Integrodifferential equations Periodic boundary value problems Carathéodory conditions lower and upper solutions Sobolev spaces Topological degree

EXISTENCE OF solutions TO A THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

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Annals of Differential Equations 2012年第3期28卷 368-372页

作者： Lixin Zhang 1,Bo Sun 2,Chunfeng Xing 1(1.Dept.of Basic Courses,Beijing Union University,Beijing 100101 2.School of Applied Math.,Central University of Finance and Economics,Beijing 100081)

In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions.

关键词： third-order boundary value problem lower and upper solutions Green's function