含临界指数p-Kirchhoff型方程的非平凡解

NONTRIVIAL SOLUTIONS FOR P-KIRCHHOFF TYPE EQUATIONS INVOLVING CRITICAL EXPONENT

本文研究了一类含临界指数的p-Kirchhoff型方程.利用变分方法与集中紧性原理,通过证明对应的能量泛函满足局部的(PS)_c条件,得到了这类方程非平凡解的存在性,推广了关于Kirchhoff型方程的相关结果.

In this paper,we are concerned with the existence of nontrivial solutions to a class of p-Kirchhoff type equations involving critical exponent.By analyzing the effect of critical nonlinear term and estimating energy functional carefully,with the aid of variational methods and the concentration-compactness principle,we establish the existence of nontrivial solutions for the p-Kirchhoff type equations,which extends the results of the Kirchhoff type equations.