Existence of many sign-changing nonradial solutions for semilinear elliptic problems on thin annuli
Słowa kluczowe
Dirichlet's problem, superlinear, subcritical, sign-changing nonradial solution, group action, symmetric criticality lemma, variational methodAbstrakt
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, < i> A minmax principle, index of the critical point, and existence of sign-changing solutions to elliptic boundary value problems< /i> , Electron. J. Differential Equations < b> 2< /b> (1998), 1–18]).Pobrania
Opublikowane
1999-06-01
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CASTRO, Alfonso & FINAN, Marcel B. Existence of many sign-changing nonradial solutions for semilinear elliptic problems on thin annuli. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 1999, T. 13, nr 2, s. 273–279. [udostępniono 23.9.2024].
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