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Variational analysis for a nonlinear elliptic problem on theSierpiński gasket

Published online by Cambridge University Press:  16 January 2012

Gabriele Bonanno,
Giovanni Molica Bisci and
Vicenţiu Rădulescu
Gabriele Bonanno
Affiliation:
Department of Science for Engineering and Architecture (Mathematics Section) Engineering Faculty, University of Messina, 98166 Messina, Italy. bonanno@unime.it
Giovanni Molica Bisci
Affiliation:
Dipartimento MECMAT, University of Reggio Calabria, Via Graziella, Feo di Vito, 89124 Reggio Calabria, Italy; gmolica@unirc.it
Vicenţiu Rădulescu
Affiliation:
Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, RomaniaDepartment of Mathematics, University of Craiova, Street A.I. Cuza No. 13, 200585 Craiova, Romania; vicentiu.radulescu@imar.ro

Abstract

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

Keywords

Sierpiński gasketnonlinear elliptic equationDirichlet formweak Laplacian

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 4 , October 2012, pp. 941 - 953
Copyright
© EDP Sciences, SMAI, 2012

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