Topological Methods in Nonlinear Analysis

Existence of many sign-changing nonradial solutions for semilinear elliptic problems on thin annuli

Alfonso Castro and Marcel B. Finan

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Abstract

We study the existence of many nonradial sign-changing solutions of a superlinear Dirichlet boundary value problem in an annulus in $\mathbb R^N$. We use Nehari-type variational method and group invariance techniques to prove that the critical points of an action functional on some spaces of invariant functions in $H_{0}^{1,2}(\Omega_{\varepsilon})$, where $\Omega_{\varepsilon}$ is an annulus in $\mathbb R^N$ of width $\varepsilon$, are weak solutions (which in our case are also classical solutions) to our problem. Our result generalizes an earlier result of Castro et al. (See [A. Castro, J. Cossio and J. M. Neuberger, A minmax principle, index of the critical point, and existence of sign-changing solutions to elliptic boundary value problems, Electron. J. Differential Equations 2 (1998), 1–18]).

Article information

Source
Topol. Methods Nonlinear Anal., Volume 13, Number 2 (1999), 273-279.

Dates
First available in Project Euclid: 29 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1475178882

Mathematical Reviews number (MathSciNet)
MR1742224

Zentralblatt MATH identifier
0952.35055

Citation

Castro, Alfonso; Finan, Marcel B. Existence of many sign-changing nonradial solutions for semilinear elliptic problems on thin annuli. Topol. Methods Nonlinear Anal. 13 (1999), no. 2, 273--279. https://projecteuclid.org/euclid.tmna/1475178882


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References

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