Existence Of High-energy Solutions To A Kirchhoff Type Equation With Slightly Supercritical Exponent

In this paper,we study the existence of a high-energy solution to the following nonlinear Kirchhoff type problem with slightly supercritical exponent,where a>0,b>0 are constants,ε>0 is a parameter,and Q(y)is a positive real-valued continuous function on R3.Under some mild assumptions on Q(y),we proved that for any strict local minimum point xo of Q(y),there exists a high-energy solution concentrating at x0 by perturbation method and reduction method.