Parametric critical point theorems and their applications to boundary value problems on the Sierpiński Gasket

2017/11/30 by Marek Galewski, Galewski, Marek, Mateusz Krukowski +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1711.11238

openalex publication_date 2017/11/30 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28

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 Sierpiński Gasket are given in presence of assumptions which lead to fulfillment of the mountain geometry.

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