## Differential and Integral Equations

### Minimal nodal solutions of a Schrödinger equation with critical nonlinearity and symmetric potential

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 16, Number 8 (2003), 981-992.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060579

Mathematical Reviews number (MathSciNet)
MR1989597

Zentralblatt MATH identifier
1161.35385

#### Citation

Clapp, Mónica; Ding, Yanheng. Minimal nodal solutions of a Schrödinger equation with critical nonlinearity and symmetric potential. Differential Integral Equations 16 (2003), no. 8, 981--992. https://projecteuclid.org/euclid.die/1356060579