Acta mathematica scientia,Series B ›› 2005, Vol. 25 ›› Issue (1): 81-88.

• Articles • Previous Articles     Next Articles

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)

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

CLC Number: 

  • 34B15
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