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On the multiplicity of nodal solutions of a prescribed mean curvature problem
Author(s) -
Bonheure Denis,
Derlet Ann,
de Valeriola Sébastien
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100263
Subject(s) - mathematics , multiplicity (mathematics) , mean curvature , degenerate energy levels , dirichlet problem , curvature , perturbation (astronomy) , mathematical analysis , dirichlet boundary condition , mathematical physics , boundary value problem , pure mathematics , geometry , physics , quantum mechanics
We prove existence and multiplicity results for sign‐changing solutions of a prescribed mean curvature equation with Dirichlet boundary conditions. Our arguments involve a perturbation of the degenerate part \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$1/\sqrt{1+s}$\end{document} , which allows us to use classical variational techniques and to localize small regular solutions.