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

Abstract

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.

Keywords

• singular elliptic equation
• kirchhoff-type nonlocal term
• critical sobolev exponent
• positive solutions
• perturbation method