This paper studies the existence of positive solutions to a class of singular elliptic problems involving the Finsler–Laplacian operator in a bounded domain \(\Omega \subset \mathbb {R}^N\) . The nonlinearity in the problem exhibits critical exponential growth, presenting significant analytical challenges. By employing the Galerkin method and leveraging a refined version of the Trudinger–Moser inequality, we establish the existence of a positive weak solution. Our approach extends beyond the classical Sobolev embedding techniques, allowing us to address the problem in a more general setting. This work not only generalizes previous results limited to \(\mathbb {R}^2\) but also provides new insights into the analysis of singular elliptic problems with critical growth, advancing the understanding of such nonlinear phenomena in higher dimensions.
