Two positive solutions for quasilinear elliptic equations with singularity and critical exponents

Boundary Value Problems

Xiaorong Luo¹  Yanbin Sang¹  Zongyuan Zhu² 

[1] Department of Mathematics, School of Science, North University of China;School of Data Sciences, Zhejiang University of Finance and Economics;

关键词: Quasilinear;    Singularity;    Critical;    Sobolev–Hardy exponent;   

DOI  :  10.1186/s13661-018-1018-7

来源: DOAJ

【 摘 要 】

Abstract In this paper, we consider the quasilinear elliptic equation with singularity and critical exponents {−Δpu−μ|u|p−2u|x|p=Q(x)|u|p∗(t)−2u|x|t+λu−s,in Ω,u>0,in Ω,u=0,on ∂Ω, $$ \textstyle\begin{cases} -\Delta_{p}u-\mu \frac{ \vert u \vert ^{p-2}u}{ \vert x \vert ^{p}}=Q(x) \frac{ \vert u \vert ^{p^{*}(t)-2}u}{ \vert x \vert ^{t}}+\lambda u^{-s}, &\text{in }\Omega , \\ u>0, & \text{in }\Omega , \\ u=0, &\text{on }\partial \Omega , \end{cases} $$ where Δp=div(|∇u|p−2∇u) $\Delta_{p}= \operatorname {div}(|\nabla u|^{p-2}\nabla u)$ is a p-Laplace operator with 1

【 授权许可】

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