SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT  

作　　者：王影 王明新 

机构地区：[1]School of Mathematics and Information Science, North China University of Water Resources and Electric Power [2]Natural Science Research Center, Harbin Institute of Technology

出　　处：《Acta Mathematica Scientia》2015年第5期1023-1036,共14页数学物理学报（B辑英文版）

基　　金：supported by the Natural Science Foundation of Henan Province(15A110050)

摘　　要：In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω, and the domain Ω is a smooth bounded open set in R^N（N≥2）. Especially, under the condition that g（x, s） = 1/｜s｜^α （α〉0） is singular at s = 0, we obtain that α 〈 p is necessary and sufficient for the existence of solutions in W0^1,p（Ω） to problem （0.1） when f is sufficiently regular.In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω, and the domain Ω is a smooth bounded open set in R^N（N≥2）. Especially, under the condition that g（x, s） = 1/｜s｜^α （α〉0） is singular at s = 0, we obtain that α 〈 p is necessary and sufficient for the existence of solutions in W0^1,p（Ω） to problem （0.1） when f is sufficiently regular.

关 键 词：quasilinear elliptic equations existence and nonexistence gradient terms singular weights 

分 类 号：O175.25[理学—数学] O221.2[理学—基础数学]