anisotropic p(.)-Laplacian

In this paper, we establish the existence of a class of discrete nonlinear systems involving the anisotropic $\vec{p}(\cdot)$-Laplacian operator using an optimization based approach.  We then simulate the solutions by implementing a deep learning model.  The numerical results demonstrate that the proposed method is stable and robust compared to conventional approaches such as the Newton–Krylov method.