Multiple Solutions of Dirichlet Problems on the Sierpinski Gasket

Brigitte E. Breckner () and Csaba Varga ()
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Brigitte E. Breckner: Babeş-Bolyai University
Csaba Varga: Babeş-Bolyai University

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 3, No 5, 842-861

Abstract: 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.

Keywords: Sierpinski gasket; Weak Laplacian; Dirichlet problem on the Sierpinski gasket; Weak solution; Critical point (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-013-0368-7

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