  In this paper we prove a version of the Fountain Theorem for a class of
nonsmooth functionals that are sum of a $C^1$ functional and a convex lower
semicontinuous functional, and also a version of a theorem due to Heinz for
this class of functionals. The new abstract theorems will be used to prove the
existence of infinitely many solutions for some elliptic problems whose the
associated energy functional is of the above mentioned type. We study problems
with logarithmic nonlinearity and a problem involving the 1-Laplacian operator.
