Existence and Concentration Phenomena for a Class of Indefinite Variational Problems with Critical Growth

摘要

In this paper we are interested to prove the existence and concentration of ground state solution for the following class of problems where N >= 2, A:Double-struck capital RN -> Double-struck capital R is a continuous function having critical growth, V:Double-struck capital RN -> Double-struck capital R is a continuous and DOUBLE-STRUCK CAPITAL ZN-periodic function with 0 is not an element of sigma(Delta + V ). By using variational methods, we prove the existence of solution for & x1d716;& xdf16; small enough. After that, we show that the maximum points of the solutions concentrate around of a maximum point of A.