EXISTENCE AND CONCENTRATION RESULTS FOR KIRCHHOFF-TYPE SCHRODINGER SYSTEMS WITH STEEP POTENTIAL WELL

In this paper, we consider the following Kirchhoff-type Schrodinger system -(a(1) + b(1) integral(R3) \del u\(2)dx) Delta u + gamma V(x)u = 2 alpha/alpha + beta\u\(alpha-2)u\v\(beta) in R-3, -(a(2) + b(2) integral(R3) \del v\(2)dx) Delta v + gamma W(x)v = 2 beta/alpha + beta\u\(alpha)\v\(beta-2)v in R-3, u, v is an element of H-1(R-3), where a(i) and b(i) are positive constants for i = 1,2, gamma > 0 is a parameter, V(x) and W(x) are nonnegative continuous potential functions. By applying the Nehari manifold method and the concentration-compactness principle, we obtain the existence and concentration of ground state solutions when the parameter gamma is sufficiently large.