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

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.