On some nonhomogeneous elliptic problems

This thesis is devoted to investigating the existence of positive solutions to Dirichlet problems driven by nonhomogeneous differential operators, inspired by the $(p,q)$-Laplacian. These operators include the $\Lambda$-Laplacian, where $\Lambda$ is a Young function, double-phase operators, and fractional competing operators. Due to the nonhomogeneous nature of the governing operators, the existence of solutions is established through approximation and/or normalization procedures, truncation techniques, variational and/or topological methods.