Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket

¹ Department of Science for Engineering and Architecture (Mathematics Section) Engineering Faculty, University of Messina, 98166 Messina, Italy
bonanno@unime.it
² Dipartimento MECMAT, University of Reggio Calabria, Via Graziella, Feo di Vito, 89124 Reggio Calabria, Italy
gmolica@unirc.it
³ Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
⁴ Department of Mathematics, University of Craiova, Street A.I. Cuza No. 13, 200585 Craiova, Romania
vicentiu.radulescu@imar.ro

Received: 14 April 2011
Revised: 11 November 2011

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.