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Multiple Solutions of Dirichlet Problems on the Sierpinski Gasket

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Abstract

There are treated nonlinear, elliptic, and parameter-depending problems, defined on the Sierpinski gasket, a highly non-smooth fractal set. Even if the structure of this fractal differs considerably from that of (open) domains of Euclidean spaces, the paper emphasizes that PDEs defined on it may be studied (as in the Euclidean case) by means of certain variational methods. Using such methods, and some recent abstract multiplicity theorems by B. Ricceri, there are proved several results concerning the existence of multiple solutions of three-parameter Dirichlet problems defined on the Sierpinski gasket.

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Acknowledgements

Csaba Varga was supported by the grant PN-II-ID-PCE-2011- 3-0241 awarded by CNCS-UEFISCDI, the Romanian National Authority for Scientific Research.

The authors would like to thank Professor Biagio Ricceri for his helpful suggestions.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Kogălniceanu str. 1, 400084, Cluj-Napoca, Romania

    Brigitte E. Breckner & Csaba Varga

Authors
  1. Brigitte E. Breckner
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  2. Csaba Varga
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Correspondence to Brigitte E. Breckner.

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Breckner, B.E., Varga, C. Multiple Solutions of Dirichlet Problems on the Sierpinski Gasket. J Optim Theory Appl 167, 842–861 (2015). https://doi.org/10.1007/s10957-013-0368-7

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  • DOI: https://doi.org/10.1007/s10957-013-0368-7

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