全空间中一类Kirchhoff方程非平凡弱解的存在性

Existence of nontrivial weak solution for a class of Kirchhoff-type equation in

考虑如下Kirchhoff方程:-(a+b∫RN|▽u|2dx)△u=V(x)u=f(x,u),x∈RN(E)非平凡弱解的存在性问题,利用临界点理论中的山路引理,方程(E)弱解的存在性结果被证明。

In this paper,we concern with a class of Kirchhoff-type problems as follows：By using the Mountain Pass Theorem in Critical point theory we obtain a new existence result of nontrivial weak solution for the problem.