Existence of multi-bump solutions for a semilinear Schrödinger–Poisson system

In this paper, we study the existence of multi-bump solutions for the semilinear Schrödinger–Poisson system where p ∈ (1, 5), a, b element of C(R3) and a(x) > 0, b(x) > 0 in R3. For any positive integer K, we prove that there exists ε(K) > 0 such that, for 0 < ε < ε(K), the system has a K-bump solution. Then the equation has more and more multi-bump solutions as ε → 0. (paper)