Parametric critical point theorems and their applications to boundary value problems on the Sierpi\'nski Gasket
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\'nski Gasket are given in presence of assumptions which lead to fulfillment of the mountain geometry.
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