SIGN CHANGING SOLUTIONS OF NONLINEAR SCHRÖDINGER EQUATIONS

Abstract. We are interested in solutions u ∈ H1(RN) of the linear Schrö-dinger equation −δu+bλ(x)u = f(x, u). The nonlinearity f grows superlin-early and subcritically as |u | → ∞. The potential bλ is positive, bounded away from 0, and has a potential well. The parameter λ controls the steep-ness of the well. In an earlier paper we found a positive and a negative solution. In this paper we find third solution. We also prove that this third solution changes sign and that it is concentrated in the potential well if λ→∞. No symmetry conditions are assumed. 1