Least energy solutions for a quasilinear Schrodinger equation with potential well

In this paper, we consider the existence of least energy solutions for the following quasilinear Schrodinger equation: -Delta u + (lambda alpha(x) + 1) u - 1/2 (Delta vertical bar u vertical bar(2))u = f (u), x is an element of R-N, (E-lambda) with a(x) >= 0 having a potential well, where N >= 3 and lambda > 0 is a parameter. Under suitable hypotheses, we obtain the existence of a least energy solution u(lambda) of (E-lambda) which localizes near the potential well int a(-1)(0) for lambda large enough by using the variational method and the concentration compactness method in an Orlicz space.