On nonlinear elliptic problems with discontinuities

Antonella Fiacca; Nikolaos Matzakos; Nikolaos S. Papageorgiou

Displaying similar documents to “On nonlinear elliptic problems with discontinuities”

Multiple solutions for nonlinear discontinuous elliptic problems near resonance

Nikolaos Kourogenis, Nikolaos Papageorgiou (1999)

Colloquium Mathematicae

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We consider a quasilinear elliptic eigenvalue problem with a discontinuous right hand side. To be able to have an existence theory, we pass to a multivalued problem (elliptic inclusion). Using a variational approach based on the critical point theory for locally Lipschitz functions, we show that we have at least three nontrivial solutions when $λ \to λ_{1}$ from the left, $λ_{1}$ being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.

Multivalued nonpositone problems

David Arcoya, Marco Calahorrano (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this note, the existence of non-negative solutions for some multivalued non-positone elliptic problems is studied.

On quasilinear elliptic equations in $ℝ^{N}$ .

Alves, C.O., Concalves, J.V., Maia, L.A. (1996)

Abstract and Applied Analysis

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Strongly nonlinear elliptic boundary value problems

H. Brézis, F. E. Browder (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On some elliptic boundary-value problems with discontinuous nonlinearities

Giovanni Anello (2005)

Annales Polonici Mathematici

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We establish two existence results for elliptic boundary-value problems with discontinuous nonlinearities. One of them concerns implicit elliptic equations of the form ψ(-Δu) = f(x,u). We emphasize that our assumptions permit the nonlinear term f to be discontinuous with respect to the second variable at each point.

Quasilinear elliptic problems with nonmonotone discontinuities and measure data.

Liang, Jin, Rodrigues, José Francisco (1996)

Portugaliae Mathematica

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On a comparison principle for a quasilinear elliptic boundary value problem of a nonmonotone type

Michal Křížek, Liping Liu (1996)

Applicationes Mathematicae

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A nonlinear elliptic partial differential equation with the Newton boundary conditions is examined. We prove that for greater data we get a greater weak solution. This is the so-called comparison principle. It is applied to a steady-state heat conduction problem in anisotropic magnetic cores of large transformers.

Eigenvalue problems of quasilinear elliptic systems on R.

Gong Bao Li (1987)

Revista Matemática Iberoamericana

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In this paper we get the existence results of the nontrivial weak solution (λ,u) of the following eigenvalue problem of quasilinear elliptic systems -D_α (a_αβ(x,u) D_βuⁱ) + 1/2 D_uⁱ a_αβ(x,u)D_αu^j D_βu^j + h(x) uⁱ = ...

On Monotone and Schwarz Alternating Methods for Nonlinear Elliptic PDEs

Shiu-Hong Lui (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known...