Parametric critical point theorems and their applications to boundary value problems on the Sierpi\'{n}ski Gasket
Classical Analysis and ODEs
2017-12-01 v1
Abstract
In this note we consider the classical variational tools like: Ekelenad's Variational Principle, Mountain Pass Lemma and some of their corollaries subject to a parameter. Next, we investigate the behaviour of critical points obtained once a sequence of parameters is allowed to be convergent. Applications for the Dirichlet Boundary Value Problem on the Sierpi\'{n}ski Gasket are given in presence of assumptions which lead to fulfillment of the mountain geometry.
Keywords
Cite
@article{arxiv.1711.11238,
title = {Parametric critical point theorems and their applications to boundary value problems on the Sierpi\'{n}ski Gasket},
author = {Marek Galewski and Mateusz Krukowski},
journal= {arXiv preprint arXiv:1711.11238},
year = {2017}
}