EuDML | Browse

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 $λ_{n} \to \infty$ .

Eigenvalue questions on some quasilinear elliptic problems

Poulou, M. N., Stavrakakis, N. M. (2007)

Proceedings of Equadiff 11

Eigenvalues of the $p$ -Laplacian in $𝐑^{N}$ with indefinite weight

Yin Xi Huang (1995)

Commentationes Mathematicae Universitatis Carolinae

We consider the nonlinear eigenvalue problem $- {div (| \nabla u |}^{p - 2} {\nabla u) = λ g (x) | u |}^{p - 2} u$ in $𝐑^{N}$ with $p > 1$ . A condition on indefinite weight function $g$ is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in $W^{1, p} (𝐑^{N})$ . A nonexistence result is also given for the case $p \geq N$ .

Éléments finis et problèmes elliptiques dégénérés

J. M. Thomas, M. Crouzeix (1973)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Elliptic and degenerate-elliptic operators in unbounded domains

D. E. Edmunds, W. D. Evans (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Elliptic equations with decreasing nonlinearity I: barrier method for decreasing solutions

Tadie (1998)

Proceedings of Equadiff 9

Elliptic equations with decreasing nonlinearity II: radial solutions for singular equations

Tadie (1998)

Proceedings of Equadiff 9

Entire solutions to a class of fully nonlinear elliptic equations

Ovidiu Savin (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study nonlinear elliptic equations of the form $F (D^{2} u) = f (u)$ where the main assumption on $F$ and $f$ is that there exists a one dimensional solution which solves the equation in all the directions $ξ \in ℝ^{n}$ . We show that entire monotone solutions $u$ are one dimensional if their $0$ level set is assumed to be Lipschitz, flat or bounded from one side by a hyperplane.

Équations elliptiques fuchsiennes du second ordre et valeurs propres asymptotiques (suite)

F. Treves (1974/1975)

Séminaire Équations aux dérivées partielles (Polytechnique)

Équations elliptiques fuchsiennes du second ordre et valeurs propres asymptotiques

F. Treves (1974/1975)

Séminaire Équations aux dérivées partielles (Polytechnique)

Equations of mean curvature type on exterior domains.

I. Walter-Koch (1998)

Manuscripta mathematica

Estimates for smooth absolutely minimizing Lipschitz extensions.

Evans, Lawrence C. (1993)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Estimates on elliptic equations that hold only where the gradient is large

Cyril Imbert, Luis Silvestre (2016)

Journal of the European Mathematical Society

We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Hölder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.

Estimation d'erreur optimale et de type superconvergence de la méthode des éléments finis pour un problème aux limites, dégénéré

Mohamed El Hatri (1987)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Estimation du peste dans la théorie spectrale d' une classe de problèmes d'opérateurs elliptiques dégénérés

Pham The Lai (1975/1976)

Séminaire Équations aux dérivées partielles (Polytechnique)

Currently displaying 1 – 20 of 50

Page 1 Next