Bulletin of the Australian Mathematical Society

Table of Contents - June 2012 - Volume 85, Issue 03  

Research Article

TWO NONTRIVIAL WEAK SOLUTIONS FOR THE DIRICHLET PROBLEM ON THE SIERPIŃSKI GASKET

DENISA STANCU-DUMITRUa1

a1 Department of Mathematics, University of Craiova, 200585 Craiova, Romania (email: denisa.stancu@yahoo.com)

Abstract

We study a Dirichlet problem involving the weak Laplacian on the Sierpiński gasket, and we prove the existence of at least two distinct nontrivial weak solutions using Ekeland’s Variational Principle and standard tools in critical point theory combined with corresponding variational techniques.

(Received June 06 2011)

2010 Mathematics subject classification

  • primary 28A80; secondary 35B38;
  • 35J05;
  • 31C25

Keywords and phrases

  • Sierpiński gasket;
  • weak Laplacian;
  • Dirichlet form;
  • weak solution;
  • Ekeland’s variational principle

Footnotes

This work was partially supported by the strategic grant POSDRU/88/1.5/S/49516, Project ID 49516 (2009), co-financed by the European Social Fund–Investing in People, within the Sectorial Operational Programme Human Resources Development 2007–2013. The author was also partially supported by the grant CNCSIS-UEFISCSU PN-II-ID-PCE-2011-3-0075 Analysis, Control and Numerical Approximations of Partial Differential Equations.