奇异四阶周期边值问题的正解

Abstract

Abstract:

The purpose of this paper is to study the positive solutions to a class of nonlinear fourth-order periodic boundary value problems, where the nonlinear term f(t, u) is allowed to be singular at t = 0, t = 1 and u = 0. By introducing the height functions of nonlinear term and considering the integrations of the height functions, the growths of nonlinear term on some bounded sets are described. By applying the Hammerstein integral equations and the
Guo-Krasnoselskii fixed point theorem of cone expansion-compression type, some new theorems concerned with the existence and multiplicity of positive solutions are obtained

Key words: Singular ordinary differential equatio, Periodic boundary value problem, Positive solution, Existence, Multiplicity

CLC Number:

34B16

TAO Qiang-Liu. Positive Solutions of Singular Fourth-order Periodic Boundary Value Problems[J].Acta mathematica scientia,Series A, 2011, 31(3): 594-601.

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Positive Solutions of Singular Fourth-order Periodic Boundary Value Problems

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