具p-Laplacian算子型奇异边值问题正解的存在性

The Existence of Positive Solutions of Singular Boundary Value Problems with p-Laplacian

讨论了一类具 p- Laplacian算子型奇异边值问题 (Φp( x′) )′+α( t) f ( x( t) ) =0 ,x( 0 ) -βx′( 0 ) =0 ,x( 1 ) +δx′( 1 ) =0正解的存在性 ,其中Φp( x) =| x| p- 2 x,p>1 .通过使用不动点指数定理 ,在适当的条件下 ,建立了这类边值问题存在一个和多个正解的充分条件 .这些结果能被用来研究椭圆边值问题径向对称解的存在性 .

In this paper, the authors discuss the existence of positive solutions for a singular boundary value problems with p-Laplacian (Φ p(x′))′+a(t)f(x(t))=0,x(0)-βx′(0)=0,x(1)+δx′(1)=0,where Φ p(x)=|x| p-2 ,p>1. By using the fixed point index theorem the authors established the sufficient conditions of the existence of positive solutions for this boundary value problems under some conditions.These results can be applied to study the existence of the radial solutions for the elliptic boundary value problems.