Existence of Positive Solutions for Kirchhoff Type Problems with Critical Exponent

摘要

In this paper,we consider the following Kirchhoff type problem with critical exponent {-（a+b∫Ω|▽u|2dx）△u=λuq+u5,inΩ,u=0, on (3)Ω,}where Ω (∈) R3 is a bounded smooth domain,0 ＜ q ＜ 1 and the parameters a,b,λ ＞ 0.We show that there exists a positive constant T4(a) depending only on a,such that for each a ＞ 0 and 0 ＜ λ ＜ T4(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.