  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.
