SIGN-CHANGING MULTI-BUMP SOLUTIONS FOR CHOQUARD EQUATION WITH DEEPENING POTENTIAL WELL

In this paper, we are concerned with the existence of signchanging multi-bump solutions for the following nonlinear Choquard equation (0.1) -Delta u + (lambda V (x) + 1)u = (I-alpha * |u|(p))|u|(p) (2)u in R-N, where I-alpha is the Riesz potential, lambda is an element of R+, (N - 4)(+) < alpha < N, 2 <= p < (N + alpha)=(N-2), and V (x) is a nonnegative continuous function with a potential well Omega := int(V-1 (0)) which possesses k disjoint bounded components Omega(1),...,Omega(k). We prove the existence of sign-changing multi-bump solutions for (0.1) if lambda is large enough.