Existence of positive solutions for a semilinear Schrodinger equation in RN

In this paper, we study the existence of multi-bump solutions for the semilinear Schrodinger equation -Delta u + (1 + lambda a(x))u = (1 -lambda b(x))vertical bar u vertical bar(p-2)u, for all u is an element of H-1(R-N), where N >= 1, 2 < p < 2N/(N - 2) if N >= 3, p > 2 if N = 2 or N = 1, a(x) is an element of C(R-N) and a(x) > 0, b(x) is an element of C(R-N) and b(x) > 0. For any n is an element of N, we prove that there exists lambda(n) > 0 such that, for 0 < lambda < lambda(n), the equation has an n-bump positive solution. Moreover, the equation has more and more multi-bump positive solutions as lambda -> 0.