SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT

被引：5

作者：

Wang, Ying ^{[1
]}

Wang, Mingxin ^{[2
]}

机构：

[1] North China Univ Water Resources & Elect Power, Sch Math & Informat Sci, Zhengzhou 450011, Peoples R China

[2] Harbin Inst Technol, Ctr Sci Res, Harbin 150080, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2015年 / 35卷 / 05期

关键词：

quasilinear elliptic equations; existence and nonexistence; gradient terms; singular weights; QUASI-LINEAR EQUATIONS; NATURAL GROWTH TERMS; QUADRATIC GROWTH; P-GROWTH; EXISTENCE;

D O I：

10.1016/S0252-9602(15)30036-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we consider existence and nonexistence of solutions to problem {-Delta(p)u + g(x, u)vertical bar del ur vertical bar(p) = f in Omega, (0.1) u = 0 in partial derivative Omega, with 1 < p < infinity, where f is a positive measurable function which is bounded away from 0 in Omega, and the domain Omega is a smooth bounded open set in R-N (N >= 2). Especially, under the condition that g(x, s) = 1/vertical bar s vertical bar(alpha) (alpha > 0) is singular at alpha = 0, we obtain that alpha < p is necessary and sufficient for the existence of solutions in W-0(1,p)(Omega) to problem (0.1) when f is sufficiently regular.

引用

页码：1023 / 1036

页数：14

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