A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.

Julián Fernández Bonder; Julio D. Rossi

Displaying similar documents to “A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.”

Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems

J. Fleckinger, J. Hernández, F. Thélin (2004)

Bollettino dell'Unione Matematica Italiana

Similarity:

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.

Equality in Wielandt’s eigenvalue inequality

Shmuel Friedland (2015)

Special Matrices

Similarity:

In this paper we give necessary and sufficient conditions for the equality case in Wielandt’s eigenvalue inequality.

On the existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems.

Jacqueline Fleckinger, Jesús Hernández, François De Thélin (2003)

RACSAM

Similarity:

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 inverse of the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case. ...

Eigenvalue problems with indefinite weight

Andrzej Szulkin, Michel Willem (1999)

Studia Mathematica

Similarity:

We consider the linear eigenvalue problem -Δu = λV(x)u, $u \in D_{0}^{1, 2} (Ω)$ , and its nonlinear generalization $- Δ_{p} u = λ V (x) {| u |}^{p - 2} u$ , $u \in D_{0}^{1, p} (Ω)$ . The set Ω need not be bounded, in particular, $Ω = ℝ^{N}$ is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues $λ_{n} \to \infty$ .

Isolation and simplicity for the first eigenvalue of the $p$ -Laplacian with a nonlinear boundary condition.

Martínez, Sandra, Rossi, Julio D. (2002)

Abstract and Applied Analysis

Similarity:

Dependence of a differential equation on the first eigenvalue of a suitable problem

Jan Bochenek (1980)

Annales Polonici Mathematici

Similarity:

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

Karim Chaïb (2002)

Publicacions Matemàtiques

Similarity:

The purpose of this paper is to extend the Díaz-Saá’s inequality for the unbounded domains as R^N. 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...

A maxmin principle for nonlinear eigenvalue problems with application to a rational spectral problem in fluid-solid vibration

Heinrich Voss (2003)

Applications of Mathematics

Similarity:

In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction.

Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string

Behrouz Emamizadeh, Amin Farjudian (2014)

Nonautonomous Dynamical Systems

Similarity:

In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the difference between the densities of the two materials is sufficiently small. Finally, a simple numerical algorithm will be presented which will...