Periodic Positive Solution to a Class of Singular Second-Order Ordinary Differential Equations

被引：6

作者：

Yao, Qingliu ^{[1
]}

机构：

[1] Nanjing Univ Finance & Econ, Dept Appl Math, Nanjing 210003, Peoples R China

来源：

ACTA APPLICANDAE MATHEMATICAE | 2010年 / 110卷 / 02期

关键词：

Singular ordinary differential equation; Periodic boundary value problem; Positive solution; Fixed point theorem; BOUNDARY-VALUE-PROBLEMS; EXISTENCE; 2ND; THEOREM;

D O I：

10.1007/s10440-009-9482-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the existence of a positive solution to the second-order periodic boundary value problem u ''(t) + lambda(t)u(t) = f(t, u(t)), 0 < t < 2 pi, u(0) = u(2 pi), u'(0) = u'(2p), where the nonlinear term f (t, u) may be singular at t = 0, t = 2 pi and u = 0. When there exist the limit functions lim(u ->+0) f (t, u)/u and lim(u ->+infinity) f (t, u)/u, we prove that the problem has a positive solution provided that the integrations of the limit functions are appropriate.

引用

页码：871 / 883

页数：13

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