奇异四阶周期边值问题的正解

数学物理学报 ›› 2011, Vol. 31 ›› Issue (3): 594-601.

奇异四阶周期边值问题的正解

姚庆六

南京财经大学应用数学系南京 210003

收稿日期:2009-11-28 修回日期:2010-10-15 出版日期:2011-06-25 发布日期:2011-06-25
基金资助:
国家自然科学基金(11071109)资助

Positive Solutions of Singular Fourth-order Periodic Boundary Value Problems

TAO Qiang-Liu

Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003

Received:2009-11-28 Revised:2010-10-15 Online:2011-06-25 Published:2011-06-25
Supported by:
国家自然科学基金(11071109)资助

摘要/Abstract

摘要：

该文的目的是研究一类非线性四阶周期边值问题的正解, 其中允许非线性项 $f(t,u)$ 在 $t=0,~t=1$ 和 $u=0$ 处奇异. 通过引入非线性项的高度函数并且考察这些高度函数的积分, 描述了非线性项在某些有界集合上的增长. 利用Hammerstein 积分方程及锥拉伸锥压缩型的 Guo-Krasnoselskii 不动点定理, 获得了若干新的正解存在与多解定理.

关键词: 奇异常微分方程, 周期边值问题, 正解, 存在性, 多解性

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

中图分类号:

34B16

姚庆六. 奇异四阶周期边值问题的正解[J]. 数学物理学报, 2011, 31(3): 594-601.

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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