@Article{JPDE-25-187,
author = {Sun , Yijing and Liu , Xing},
title = {Existence of Positive Solutions for Kirchhoff Type Problems with Critical Exponent},
journal = {Journal of Partial Differential Equations},
year = {2012},
volume = {25},
number = {2},
pages = {187--198},
abstract = {<p>In this paper,we consider the following Kirchhoff type problemwith critical exponent&nbsp; $-(a+b∫_Ω|∇u|^2dx)Δu=λu^q+u^5, in\ Ω, &nbsp;u=0, on\ ∂Ω$, &nbsp;where $Ω⊂R^3$ is a bounded smooth domain, $0&lt; q &lt; 1$ and the parameters $a,b,λ &gt; 0$. We show that there exists a positive constant $T_4(a)$ depending only on a, such that for each $a &gt; 0$ and $0 &lt; λ &lt; T_4(a)$, the above problem has at least one positive solution. The method we used here is based on the Nehari manifold, Ekeland&#39;s variational principle and the concentration compactness principle.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v25.n2.5},
url = {http://global-sci.org/intro/article_detail/jpde/5182.html}
}