Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities

In this paper we study the existence and concentration behaviors of positive solutions to the Kirchhoff type equations -epsilon M-2(epsilon(2-N) integral(RN) vertical bar del u vertical bar(2) dx) Delta u + V(x)u = f(u) in R-N, u is an element of H-1(R-N), N >= 1, where M and V are continuous functions. Under suitable conditions on M and general conditions on f, we construct a family of positive solutions (u epsilon)epsilon is an element of(0,(epsilon) over tilde] which concentrates at a local minimum of V after extracting a subsequence (epsilon(k)).