Multiple Solutions For A Modified Kirchhoff-type Equation In R~N

In this paper, we study the following modified Kirchhoff-type equations of the form where a>0, b≥0, h E C(RN×R,R) and V E C(RN,R). Under appropriate assumptions on V(x) and h(x,u), some existence results for positive solutions, neg-ative solutions and sequence of high energy solutions are obtained via a perturbation method.