Multi-bump solutions for a strongly indefinite semilinear Schrodinger equation without symmetry or convexity assumptions

In this paper, we study the following semilinear Schrodinger equations with periodic coefficient: -Delta u + V(x)u = f(x, u), u is an element of H-1 (R-N). The functional corresponding to this equation possesses strongly indefinite structure. The nonlinear term f(x,t) satisfies some superlinear growth conditions and need not be odd or increasing in t. Using a new variational reduction method and a generalized Morse theory, we proved that this equation has infinitely many geometrically different solutions . Furthermore, if the solutions of this equation under some energy level are isolated, then we can show that this equation has infinitely many m-bump solutions for any positive integer m >= 2. (C) 2007 Elsevier Ltd. All rights reserved.