关键词: p-Laplacian算子;奇异边值问题;正解;不动点指数

Abstract:

In this paper, the authors discuss the existence of positive solu tions 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 problem s under some conditions.These results can be applied to study the existence of the radial solutions for the elliptic boundary value problems.
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Key words: p-Laplacian operator, Singular boundary value p roblems, Positive solutions, Fixed point index