Nonlinear problems on the Sierpi\'nski gasket
Analysis of PDEs
2017-07-04 v1 Operator Algebras
Optimization and Control
Abstract
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).
Cite
@article{arxiv.1705.10111,
title = {Nonlinear problems on the Sierpi\'nski gasket},
author = {Giovanni Molica Bisci and Dušan D. Repovš and Raffaella Servadei},
journal= {arXiv preprint arXiv:1705.10111},
year = {2017}
}