INFINITELY MANY POSITIVE SOLUTIONS FOR THE NONLINEAR SCHRODINGER POISSON SYSTEM

We consider the following nonlinear Schrodinger-Poisson system in R-3 {-Delta u + u + K(vertical bar y vertical bar)Phi(y)u = Q(vertical bar y vertical bar)vertical bar u vertical bar(p-1)u, y is an element of R-3, -Delta Phi= K(vertical bar y vertical bar)u(2), y is an element of R-3, (0.1) where K(r) and Q(r) are bounded and positive functions, 1 < p < 5. Assume that K(r) and Q(r) have the following expansions (as r -> +infinity): K(r) = a/r(m) + O (1/r(m+theta)), Q(r) = Q(0) + b/r(n) + O(1/r(n+kappa)), where a > 0, b is an element of R, m > 1/2, n > 1, theta > 0, kappa > 0, and Q(0) > 0 are some constants. We prove that (0.1) has infinitely many non-radial positive solutions if b < 0, or if b >= 0 and 2m < n.