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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Published in | Electronic journal of qualitative theory of differential equations Vol. 2018; no. 100; pp. 1 - 20 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
University of Szeged
01.01.2018
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Subjects | |
Online Access | Get full text |
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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, $a,b,\lambda>0,~0<\gamma<1$ 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. |
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ISSN: | 1417-3875 1417-3875 |
DOI: | 10.14232/ejqtde.2018.1.100 |