Sign Changing Solutions of Superlinear Schrödinger Equations
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- 1 January 2005
- journal article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 29 (1-2) , 25-42
- https://doi.org/10.1081/pde-120028842
Abstract
We are interested in solutions u 2 H1(RN) of the linear Schro- dinger equation u +b (x)u = f(x,u). The nonlinearity f grows superlin- early and subcritically as |u| ! 1. The potential b is positive, bounded away from 0, and has a potential well. The parameter 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 ! 1. No symmetry conditions are assumed.Keywords
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