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Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.

Variational and topological methods for Dirichlet problems with $p$ -Laplacian.

Dinca, G., Jebelean, P., Mawhin, J. (2001)

Portugaliae Mathematica. Nova Série

Variational and topological methods for operator equations involving duality mappings on Orlicz-Sobolev spaces.

Dinca, George, Matei, Pavel (2007)

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

Variational characterization of interior interfaces in phase transition models on convex plane domains.

Garza-Hume, Clara E., Padilla, Pablo (2003)

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

Variational inequalities for energy functionals with nonstandard growth conditions.

Fuchs, Martin, Li, Gongbao (1998)

Abstract and Applied Analysis

Variational inequalities for vector-valued functions.

S. Hildebrandt, K.-O. Widman (1979)

Journal für die reine und angewandte Mathematik

Variational methods and linearization tools towards the spectral analysis of the $p$ -Laplacian, especially for the Fredholm alternative.

Takáč, Peter (2010)

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

Variational methods for a resonant problem with the $p$ -Laplacian in $ℝ^{N}$ .

Alziary, Benedicte, Fleckinger, Jacqueline, Takáč, Peter (2004)

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

Variational problems in domains with cusp points

Alexander Ženíšek (1993)

Applications of Mathematics

The finite element analysis of linear elliptic problems in two-dimensional domains with cusp points (turning points) is presented. This analysis needs on one side a generalization of results concerning the existence and uniqueness of the solution of a constinuous elliptic variational problem in a domain the boundary of which is Lipschitz continuous and on the other side a presentation of a new finite element interpolation theorem and other new devices.

Variational problems on classes of rearrangements and multiple configurations for steady vortices

G. R. Burton (1989)

Annales de l'I.H.P. Analyse non linéaire

Variational problems with pointwise constraints on the derivatives.

Molle, Riccardo, Passaseo, Donato (1999)

Journal of Convex Analysis

Various representations for the system of hyperbolic equations with singular coefficients.

Nasim, Adib Adel (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

Varying domains in a general class of sublinear elliptic problems.

Cano-Casanova, Santiago, López-Gómez, Julián (2004)

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

Vertex centred Discretization of Two-Phase Darcy flows on General Meshes

Robert Eymard, Cindy Guichard, Raphaèle Herbin, Roland Masson (2012)

ESAIM: Proceedings

This paper concerns the discretization of multiphase Darcy flows, in the case of heterogeneous anisotropic porous media and general 3D meshes used in practice to represent reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred approach is introduced in this paper. This scheme extends the Vertex Approximate Gradient scheme (VAG), already introduced for single phase diffusive problems in [9], to multiphase Darcy flows....

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