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
Similarity:
Displaying similar documents to “Simplicity and stability of the first eigenvalue of a nonlinear elliptic system.”
Isolation and simplicity for the first eigenvalue of the -Laplacian with a nonlinear boundary condition.
Supercritical elliptic problems in domains with small holes
Manuel del Pino, Juncheng Wei (2007)
Annales de l'I.H.P. Analyse non linéaire
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 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...
A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.
Julián Fernández Bonder, Julio D. Rossi (2002)
Publicacions Matemàtiques
Similarity:
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...
The first eigenvalue for the -Laplacian operator.
Ly, Idrissa (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Similarity:
Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue
Dimitri Mugnai (2010)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We give the precise behaviour of some solutions of a nonlinear elliptic B.V.P. in a bounded domain when a parameter approaches an eigenvalue of the principal part. If the nonlinearity has some regularity and the domain is for example convex, we also prove a nonlinear version of Courant's Nodal theorem.
Eigenvalue problems of quasilinear elliptic systems on R.
Gong Bao Li (1987)
Revista Matemática Iberoamericana
Similarity:
In this paper we get the existence results of the nontrivial weak solution (λ,u) of the following eigenvalue problem of quasilinear elliptic systems -Dα (aαβ(x,u) Dβui) + 1/2 Dui aαβ(x,u)Dαuj Dβuj + h(x) ui = ...
Existence results for classes of -Laplacian semipositone equations.
Oruganti, Shobha, Shivaji, R. (2006)
Boundary Value Problems [electronic only]
Similarity:
Positive solutions of higher order quasilinear elliptic equations.
Montenegro, Marcelo (2002)
Abstract and Applied Analysis
Similarity:
Symmetrization of functions and principal eigenvalues of elliptic operators
François Hamel, Nikolai Nadirashvili, Emmanuel Russ (2011-2012)
Séminaire Laurent Schwartz — EDP et applications
Similarity:
In this paper, we consider shape optimization problems for the principal eigenvalues of second order uniformly elliptic operators in bounded domains of . We first recall the classical Rayleigh-Faber-Krahn problem, that is the minimization of the principal eigenvalue of the Dirichlet Laplacian in a domain with fixed Lebesgue measure. We then consider the case of the Laplacian with a bounded drift, that is the operator , for which the minimization problem is still well posed. Next, we...