Abstract
This paper investigates the existence of weak solutions to a nonlinear elliptic system driven by distinct nonhomogeneous operators, where the nonlinearities exhibit superlinear growth and involve Hardy-type singular terms. To overcome the lack of compactness caused by the presence of the Hardy term, we establish a general version of the Brezis-Lieb convergence theorem and apply the Mountain Pass Theorem under the Cerami condition to prove the existence of a nontrivial, nonnegative weak solution. Our results extend previous works by addressing a broader class of nonhomogeneous operators.