Differential and Integral Equations

Antisymmetric solutions for the nonlinear Schrödinger equation

Janete S. Carvalho, Liliane A. Maia, and Olimpio H. Miyagaki

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In this article, we consider the nonlinear Schrödinger equation \begin{equation} -\Delta u + V(x)u=|u|^{p-1}u \quad \text{in} \quad \mathbb{R}^N. \end{equation} Here $V$ is invariant under an orthogonal involution. The basic tool employed here is the concentration--compactness principle. A theorem on existence of a solution which changes sign exactly once is given.

Article information

Differential Integral Equations, Volume 24, Number 1/2 (2011), 109-134.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations 35D05 35J20: Variational methods for second-order elliptic equations 47J30: Variational methods [See also 58Exx]


Carvalho, Janete S.; Maia, Liliane A.; Miyagaki, Olimpio H. Antisymmetric solutions for the nonlinear Schrödinger equation. Differential Integral Equations 24 (2011), no. 1/2, 109--134. https://projecteuclid.org/euclid.die/1356019047

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