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

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}^...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2018-01, Vol.2018 (100), p.1-20
Main Authors: Liu, Jiu, Hou, Ai-Jun, Liao, Jiafeng
Format: Article
Language:English
Subjects:
critical sobolev exponent
kirchhoff-type nonlocal term
perturbation method
positive solutions
singular elliptic equation
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Summary: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
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2018.1.100