数学物理学报(英文版) ›› 2005, Vol. 25 ›› Issue (1): 81-88.

• 论文 • 上一篇    下一篇

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE

孙继先,刘衍胜   

  1. Department of Mathematcis,Xuzhou Normal Uiniversity;Department of Mathematcis,Shandong  Normal Uiniversity;
  • 出版日期:2005-01-20 发布日期:2005-01-20
  • 基金资助:

    The Project Supported by the National Natural Science Foundation of China (10371066)

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE

 SUN Ji-Xian, LIU Yan-Qing   

  • Online:2005-01-20 Published:2005-01-20
  • Supported by:

    The Project Supported by the National Natural Science Foundation of China (10371066)

摘要:

This paper deals with the singular
nonlinear third-order periodic boundary value problem
$u^{\prime\prime\prime}+\r^3u = f(t, u)$, $0\l t \l 2\pi$, with
$u^{(i)}(0)= u^{(i)}(2\pi)$, $i=0, 1, 2$, where
 $\r\in (0, \f{1}{\s})$ and $f$ is singular at $t=0$, $t=1$
and $u=0$. Under
  suitable weaker conditions than those of [1], it is proved by
  constructing a special cone in $C[0, 2\pi]$ and
  employing the fixed point index theory that the
  problem has at least one or at least two positive solutions.

Abstract:

This paper deals with the singular
nonlinear third-order periodic boundary value problem
$u^{\prime\prime\prime}+\r^3u = f(t, u)$, $0\l t \l 2\pi$, with
$u^{(i)}(0)= u^{(i)}(2\pi)$, $i=0, 1, 2$, where
 $\r\in (0, \f{1}{\s})$ and $f$ is singular at $t=0$, $t=1$
and $u=0$. Under
  suitable weaker conditions than those of [1], it is proved by
  constructing a special cone in $C[0, 2\pi]$ and
  employing the fixed point index theory that the
  problem has at least one or at least two positive solutions.

Key words: Singular boundary value problem, third-order differential system;positive
solution

中图分类号: 

  • 34B15