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.
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页码：1023 / 1036
页数：14
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