Regular Article
Multiple Positive Solutions to Nonlinear Schrödinger Equations with Competing Potential Functions

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Abstract

In this paper we obtain multiple positive solutions of the nonlinear elliptic equation −h2 Δu+V(x) u=K(x) |u|p−2 u+Q(x) |u|q−2 u, xRN, 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).

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Supported by M.U.R.S.T. (40% and 60% funds) and E.E.C., Program Human Capital Mobility (Contract ERBCHRXCT 940494).