Topological Methods in Nonlinear Analysis

Sign changing solutions of nonlinear Schrödinger equations

Abstract

We are interested in solutions $u\in H^1({\mathbb R}^N)$ of the linear Schrödinger equation $-\delta u +b_{\lambda} (x) u =f(x,u)$. The nonlinearity $f$ grows superlinearly and subcritically as $\vert u\vert \to\infty$. The potential $b_{\lambda}$ is positive, bounded away from $0$, and has a potential well. The parameter $\lambda$ controls the steepness 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 $\lambda \to \infty$. No symmetry conditions are assumed.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 13, Number 2 (1999), 191-198.

Dates
First available in Project Euclid: 29 September 2016

https://projecteuclid.org/euclid.tmna/1475178878

Mathematical Reviews number (MathSciNet)
MR1742220

Zentralblatt MATH identifier
0961.35150

Citation

Bartsch, Thomas; Wang, Zhi-Qiang. Sign changing solutions of nonlinear Schrödinger equations. Topol. Methods Nonlinear Anal. 13 (1999), no. 2, 191--198. https://projecteuclid.org/euclid.tmna/1475178878

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