On singular elliptic inclusions with non–standard growth

In this paper, we prove the existence of solutions for a nonlinear elliptic problem characterized by a singularity, a multi-valued operator, and non-standard growth conditions. The analysis is set in the variable exponent Sobolev space [Formula: see text]. The main difficulty lies in handling how the singularity [Formula: see text] interacts with the maximal monotone graph [Formula: see text] and the variable exponent [Formula: see text]. Using a detailed regularization process and specific a priori estimates, we successfully demonstrate that a positive weak solution exists for any [Formula: see text].