MULTI-PEAK POSITIVE SOLUTIONS FOR A FRACTIONAL NONLINEAR ELLIPTIC EQUATION

In this paper we study the existence of positive multi-peak solutions to the semilinear equation epsilon(2s) (-Delta)(s) u + u = Q (x)u(p) (1), u > 0, u is an element of H-s (R-N) where (-Delta)(s) stands for the fractional Laplacian, s is an element of (0, 1), epsilon is a positive small parameter, 2 < p < 2N/N - 2s, Q (x) is a bounded positive continuous function. For any positive integer k, we prove the existence of a positive solution with k - peaks and concentrating near a given local minimum point of Q. For s - 1 this corresponds to the result of [22].