In this work, we will study the existence of non-trivial weak solutions for two classes
of elliptic and nonlinear problems, whose growth condition on these nonlinearities is
subcritical and which involve general operators of the p&q-Laplacian type.
The first problem will address the existence of non-trivial weak solutions for a general
class of eigenvalue problems, which was studied in .
In the second problem we study the existence of multiple solutions for a class of
equations similar to the previous one, by adding a perturbation to the nonlinearity. The
tecniques was motived by the thesys .
The main tools in your study are variational methods, including the classic Ekeland
Variational Principle and the Mountain Pass Theorem.