Displaying similar documents to “Isolation and simplicity for the first eigenvalue of the p -Laplacian with a nonlinear boundary condition.”

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...

Adaptive finite element analysis based on perturbation arguments

Dai, Xiaoying, He, Lianhua, Zhou, Aihui

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We review some numerical analysis of an adaptive finite element method (AFEM) for a class of elliptic partial differential equations based on a perturbation argument. This argument makes use of the relationship between the general problem and a model problem, whose adaptive finite element analysis is existing, from which we get the convergence and the complexity of adaptive finite element methods for a nonsymmetric boundary value problem, an eigenvalue problem, a nonlinear boundary...

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.

Extension of Díaz-Saá's inequality in R and application to a system of p-Laplacian.

Karim Chaïb (2002)

Publicacions Matemàtiques

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The purpose of this paper is to extend the Díaz-Saá’s inequality for the unbounded domains as RN. The proof is based on the Picone’s identity which is very useful in problems involving p-Laplacian. In a second part, we study some properties of the first eigenvalue for a system of p-Laplacian. We use Díaz-Saá’s inequality to prove uniqueness and Egorov’s theorem for the isolation. These results generalize J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis...