Multiple positive solutions to nonlinear Schrodinger equations with competing potential functions

In this paper we obtain multiple positive solutions of the nonlinear elliptic equation -h(2) Delta u + V(x) u = K(x) \u\(p-2) u + Q(x) \u\(q-2) u, x is an element of R-N, where V, K, Q are competing potential functions. We relate the number of solutions with the topology of the global minima set of a suitable ground energy function and improve a recent existence result of X. Wang and B. Zeng (1997, SIAM J. Math. Anal. 28, 633-655). (C) 2000 Academic Press.