Isolation and simplicity for the first eigenvalue of the -Laplacian with a nonlinear boundary condition.
Martínez, Sandra, Rossi, Julio D. (2002)
Abstract and Applied Analysis
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Displaying similar documents to “Regularity of the solutions for a Robin problem and some applications.”
Isolation and simplicity for the first eigenvalue of the -Laplacian with a nonlinear boundary condition.
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O'Regan, Donal (1994)
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Inequalities among eigenvalues of Sturm-Liouville problems.
Eastham, M.S.P., Kong, Q., Wu, H., Zettl, A. (1999)
Journal of Inequalities and Applications [electronic only]
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Spectral asymptotics for nonlinear multiparameter problems with indefinite nonlinearities
Tetsutaro Shibata (1999)
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A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.
Julián Fernández Bonder, Julio D. Rossi (2002)
Publicacions Matemàtiques
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In this paper we study the Sobolev trace embedding W(Ω) → L (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λ / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end...
Comparison of eigenvalues for a fourth-order four-point boundary value problem.
Karna, Basant K., Kaufmann, Eric R., Nobles, Jason (2005)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Sign-changing and extremal constant-sign solutions of nonlinear elliptic Neumann boundary value problems.
Winkert, Patrick (2010)
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Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems
J. Fleckinger, J. Hernández, F. Thélin (2004)
Bollettino dell'Unione Matematica Italiana
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We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.