Year: 2012
Author: Yijing Sun, Xing Liu
Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 2 : pp. 187–198
Abstract
In this paper,we consider the following Kirchhoff type problemwith critical exponent $-(a+b∫_Ω|∇u|^2dx)Δu=λu^q+u^5, in\ Ω, u=0, on\ ∂Ω$, where $Ω⊂R^3$ is a bounded smooth domain, $0< q < 1$ and the parameters $a,b,λ > 0$. We show that there exists a positive constant $T_4(a)$ depending only on a, such that for each $a > 0$ and $0 < λ < T_4(a)$, the above problem has at least one positive solution. The method we used here is based on the Nehari manifold, Ekeland's variational principle and the concentration compactness principle.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v25.n2.5
Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 2 : pp. 187–198
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Freedricksz transition
Author Details
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