Existence and multiplicity of non-trivial solutions for Schr?dingerKirchhoff-type equations with radial potential

摘要

In the present paper, the following Schr?dingerKirchhoff-type problem -(a+b∫R~N| ~(?u|2)dx)Δu+V(|x|)u=Q(|x|)f(u),in R ~N,u(x)~→0as |x|~(→∞), is studied. Four existence theorems of nontrivial solutions and a sequence of high energy solutions for problem (P) are obtained by the Mountain Pass Theorem and symmetric Mountain Pass Theorem.