Existence of solutions for Kirchhoff type problems with critical nonlinearity in R-N

摘要

In this paper, we consider the existence and multiplicity of standing wave solutions of Kirchhoff type problems with critical nonlinearity in : for all , where V(x) is a nonnegative potential, and K(x) is a bounded positive function. Under suitable assumptions, we show that this equation has at least one solution provided that , for any , it has m pairs of solutions if , where and are sufficiently small positive numbers. Moreover, these solutions in as epsilon -> 0.