SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT

doi:10.1016/S0252-9602(15)30036-9

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 1023-1036.doi: 10.1016/S0252-9602(15)30036-9

SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT

王影, 王明新

1. School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China;
2. Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, China

收稿日期:2014-04-08 修回日期:2015-04-25 出版日期:2015-09-01 发布日期:2015-09-01
作者简介:Ying WANG, E-mail: feelyeey@163.com; Mingxin WANG, E-mail: mxwang@hit.edu.cn
基金资助:
This research is supported by the Natural Science Foundation of Henan Province (15A110050).

SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT

Ying WANG, Mingxin WANG

1. School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China;
2. Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, China

Received:2014-04-08 Revised:2015-04-25 Online:2015-09-01 Published:2015-09-01
Supported by:
This research is supported by the Natural Science Foundation of Henan Province (15A110050).

摘要/Abstract

摘要：

In this article, we consider existence and nonexistence of solutions to problem

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

Abstract:

Key words: quasilinear elliptic equations, existence and nonexistence, gradient terms, singular weights

中图分类号:

35D05

王影, 王明新. SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT[J]. 数学物理学报(英文版), 2015, 35(5): 1023-1036.

Ying WANG, Mingxin WANG. SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT[J]. Acta mathematica scientia,Series B, 2015, 35(5): 1023-1036.

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SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT

SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT

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