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Variational analysis for a nonlinear elliptic problem on the Sierpiński 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, Romania Department of Mathematics, University of Craiova, Street A.I. Cuza No. 13, 200585 Craiova, Romania; vicentiu.radulescu@imar.ro
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Abstract

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.

Keywords

Sierpiński gasketnonlinear elliptic equationDirichlet formweak Laplacian
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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