Multiple radial symmetric solutions for nonlinear boundary value problems of -Laplacian.
Zhou, Qian, Ke, Yuanyuan (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Displaying similar documents to “Compactifications of Symmetric Spaces and Positive Eigenfunctions of the Laplacian”
Multiple radial symmetric solutions for nonlinear boundary value problems of -Laplacian.
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On the nodal set of the second eigenfunction of the laplacian in symmetric domains in
Lucio Damascelli (2000)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We present a simple proof of the fact that if is a bounded domain in , , which is convex and symmetric with respect to orthogonal directions, , then the nodal sets of the eigenfunctions of the laplacian corresponding to the eigenvalues must intersect the boundary. This result was proved by Payne in the case for the second eigenfunction, and by other authors in the case of convex domains in the plane, again for the second eigenfunction.