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:arXiv.org 2017-05
Main Authors: Giovanni Molica Bisci, Repovš, Dušan D, Servadei, Raffaella
Format: Article
Language:English
Subjects:
Banach spaces
Domains
Elliptic functions
Fractals
Theorems
Variational methods
Online Access:Get full text
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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 (1999).
ISSN:2331-8422
DOI:10.48550/arxiv.1705.10111