Existence of solutions for nonlinear elliptic singular inclusion problems

In this study we investigate the existence of solutions for a particular class of nonlinear elliptic inclusion problems involving singular terms. The analysis is carried out within a weak formulation framework, and particular attention is given to the difficulties arising from the singular nature of the nonlinearities. Using appropriate approximation methods and compactness arguments, we establish the existence of weak solutions assuming broad assumptions on the given data and the nonlinearity.