Multiplicity of positive solutions for a class of singular elliptic equations with critical Sobolev exponent and Kirchhoff-type nonlocal term

• Published in: Electronic journal of qualitative theory of differential equations Vol. 2018; no. 100; pp. 1 - 20
• Main Authors: Liu, Jiu, Hou, Ai-Jun, Liao, Jiafeng
• Format: Journal Article
• Language: English
• Published: University of Szeged 01.01.2018
• Subjects: critical sobolev exponent; kirchhoff-type nonlocal term; perturbation method; positive solutions; singular elliptic equation
• ISSN: 1417-3875; 1417-3875
• DOI: 10.14232/ejqtde.2018.1.100

We study a class of singular elliptic equations involving critical Sobolev exponent and Kirchhoff-type nonlocal term $-\big(a+b\int_{\Omega}|\nabla u|^2dx\big)\Delta u=u^{5}+g(x,u)+\lambda u^{-\gamma}$, $x\in\Omega, u>0$, $x\in\Omega$, $u=0$, $x\in\partial\Omega$, where $\Omega\subset \mathbb{R}^{3}$ is a bounded domain, $a,b,\lambda>0,~0<\gamma<1$ and $g\in C(\overline{\Omega}\times\mathbb{R})$ satisfies some conditions. By the perturbation method, variational method and some analysis techniques, we establish a multiplicity theorem.