NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF NONNEGATIVE SOLUTIONS OF INHOMOGENEOUS p-LAPLACE EQUATION  

作　　者：戴求亿 彭丽辉 

机构地区：[1]Department of Mathematics Hunan Normal University [2]Department of Mathematics Zhejiang University

出　　处：《Acta Mathematica Scientia》2007年第1期34-56,共23页数学物理学报（B辑英文版）

基　　金：This work is supported by NNSF of China (10171029).

摘　　要：Let Ω be a smooth bounded domain in R^n. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation --△pu = ｜u｜^q-1 u ＋ λf（x） on Ω, and identify necessary and sufficient conditions on Ω and f（x） which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.Let Ω be a smooth bounded domain in R^n. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation --△pu = ｜u｜^q-1 u ＋ λf（x） on Ω, and identify necessary and sufficient conditions on Ω and f（x） which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.

关 键 词：Inhomogeneous p-Laplace equation Dirichlet problem nonnegative solution 

分 类 号：O175[理学—数学]