MULTI-PEAK BOUND-STATES FOR NONLINEAR SCHRODINGER-EQUATIONS

In this paper we consider the study of standing wave solutions for a n onlinear Schrodinger equation. This problem reduces to that of finding nonnegative solutions of epsilon(2) Delta u - V (x) u + f (u) = 0 in Omega, with finite energy. Here epsilon is a small parameter, Omega is a smooth, possibly unbounded domain, f is an appropriate superlinear function. and V is a positive potential, bounded away from zero. It is the purpose of this article to obtain multi-peak solutions in the ''m ultiple well case''. We find solutions exhibiting concentration at any prescribed finite set of local minima, possibly degenerate, of the po tential. The proof relies on variational arguments, where a penalizati on-type method is developed for the identification of the desired solu tions. (C) Elsevier, Paris.