Positive solutions to a coupled singular anisotropic system with nonstandard growth and singular nonlinearities

Abstract

This paper studies a singular anisotropic system of coupled quasilinear elliptic equations. The system features anisotropic diffusion operators with variable exponents $p_i$ and $q_i$, singular terms of the form $v^{-{\gamma }_1}$ and $u^{-{\gamma }_2}$, and nonlinear source terms. By employing variational methods and an approximation problem, we prove the existence of positive solutions under suitable conditions on the nonlinearities.