Article ID Journal Published Year Pages File Type
4622854 Journal of Mathematical Analysis and Applications 2007 15 Pages PDF
Abstract

The aim of this paper is to discuss the positive solutions of the p-Laplace problem−div(|∇u|p−2∇u)+g(u)p|∇u|=λuq,−div(|∇u|p−2∇u)+g(u)|∇u|p=λuq, where p>1p>1, q>1q>1, g:[0,∞)→[0,∞) is a nonnegative continuous function, λ   is a real number. The sufficient condition to have positive solutions of the above problem is g∈L1(R+)g∈L1(R+). However, if g∉L1(R+)g∉L1(R+), there is no solution which belongs to it. Therefore, our results are optimal.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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