SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT

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

Abstract

Abstract:

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.

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

CLC Number:

35D05

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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