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2003 Minimal nodal solutions of a Schrödinger equation with critical nonlinearity and symmetric potential
Mónica Clapp, Yanheng Ding
Differential Integral Equations 16(8): 981-992 (2003).

Abstract

We study the nonlinear Schr\"{o}dinger equation \[ -\Delta u+\lambda a(x)u=\mu u+u^{2^{\ast }-1},\hbox{ \ }u\in \mathbb{R}^{N}, \] with critical exponent $2^{\ast }=2N/(N-2),$ $N\geq 4,$ where $a\geq 0$ has a potential well and is invariant under an orthogonal involution of $\mathbb{R} ^{N}$. Using variational methods we establish existence and multiplicity of solutions which change sign exactly once. These solutions localize near the potential well for $\mu $ small and $\lambda $ large.

Citation

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Mónica Clapp. Yanheng Ding. "Minimal nodal solutions of a Schrödinger equation with critical nonlinearity and symmetric potential." Differential Integral Equations 16 (8) 981 - 992, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1161.35385
MathSciNet: MR1989597

Subjects:
Primary: 35J60
Secondary: 35B33 , 35B38 , 35J20 , 35Q55 , 47J30 , 58E05

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 8 • 2003
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