ON A CLASS OF NONLOCAL SCHRODINGER EQUATIONS WITH EXPONENTIAL GROWTH

We consider the following singularly perturbed Schrodinger equation involving the N/s-fractional Laplacian operator, epsilon(N) (-Delta)(N/s)(s)u + V(x) vertical bar u vertical bar(N/s-2)u = f(u) in R-N, where epsilon is a positive parameter, s is an element of (0, 1), the potential V is positive and away from zero, and f is a Trudinger-Moser type nonlinearity. By using penalization methods and Lusternik-Schnirelmann's theory, we examine existence, multiplicity and concentration of non-trivial non-negative solutions for small values of epsilon.