Infinitely many sign-changing solutions for a Schrodinger equation in RN

In this paper, we consider a Schrodinger equation - Delta u + (lambda a(x) + 1)u = f(u). Applying Principle of Symmetric Criticality and the invariant set method, under some assumptions on a and f, we obtain an unbounded sequence of radial sign-changing solutions for the above equation in R-N when lambda > 0 large enough. As N = 4 or N >= 6, lambda > 0 given, using Fountain Theorem and the Principle of Symmetric Criticality, we prove that there exists an Unbounded sequence of non-radial sign-changing solutions for the above equation in R-N. (C) 2009 Elsevier Inc. All rights reserved.