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In this note we consider the classical variational tools like: Ekelenad'sVariational Principle, Mountain Pass Lemma and some of their corollariessubject to a parameter. Next, we investigate the behaviour of critical pointsobtained once a sequence of parameters is allowed to be convergent.Applications for the Dirichlet Boundary Value Problem on the Sierpi\'{n}skiGasket are given in presence of assumptions which lead to fulfillment of themountain geometry.

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