Sign changing solutions of nonlinear Schrödinger equations
Keywords
Nonlinear Schrödinger equation, sign changing solution, localized solution, potential well, singular limitAbstract
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.Downloads
Published
1999-06-01
How to Cite
1.
BARTSCH, Thomas and WANG, Zhi-Qiang. Sign changing solutions of nonlinear Schrödinger equations. Topological Methods in Nonlinear Analysis. Online. 1 June 1999. Vol. 13, no. 2, pp. 191 - 198. [Accessed 29 March 2024].
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