MULTI-BUMP SOLUTIONS FOR NONLINEAR CHOQUARD EQUATION WITH POTENTIAL WELLS AND A GENERAL NONLINEARITY

In this article,we study the existence and asymptotic behavior of multi-bump solutions for nonlinear Choquard equation with a general nonlinearity-Δu+(λa(x)+1)u=(1/|x|α*F(u))f(u)in R^N,where N≥3,0<α<min{N,4},λis a positive parameter and the nonnegative potential function a(x)is continuous.Using variational methods,we prove that if the potential well int(a^-1(0))consists of k disjoint components,then there exist at least 2^k-1 multi-bump solutions.The asymptotic behavior of these solutions is also analyzed asλ→+∞.