Nonlinear problems on the Sierpiński gasket

This paper concerns with a class of elliptic equations on fractal domains depending on a real parameter. Our approach is based on variational methods. More precisely, the existence of at least two non-trivial weak (strong) solutions for the treated problem is obtained exploiting a local minimum theo...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2017-08, Vol.452 (2), p.883-895
Main Authors: Molica Bisci, Giovanni, Repovš, Dušan, Servadei, Raffaella
Format: Article
Language:English
Subjects:
Fractal domains
Nonlinear elliptic equation
Sierpiński gasket
Weak Laplacian
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Summary:This paper concerns with a class of elliptic equations on fractal domains depending on a real parameter. Our approach is based on variational methods. More precisely, the existence of at least two non-trivial weak (strong) solutions for the treated problem is obtained exploiting a local minimum theorem for differentiable functionals defined on reflexive Banach spaces. A special case of the main result improves a classical application of the Mountain Pass Theorem in the fractal setting, given by Falconer and Hu in [14].
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.03.032