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arXiv · 1711.11238

Parametric critical point theorems and their applications to boundary value problems on the Sierpi\'{n}ski Gasket

Marek Galewski·Mateusz Krukowski
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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.

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Marek Galewski, Mateusz Krukowski. 2017-11-30. Parametric critical point theorems and their applications to boundary value problems on the Sierpi\'{n}ski Gasket. https://arxiv.org/abs/1711.11238

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