Competing Finsler Double Phase Equation

In this paper, we consider a representation of the competing Finsler double phase equation, i.e., a representation of the competing Finsler double phase equation in the Heisenberg groups $\mathbb{H}^{n}$. We prove the existence of a generalized variational solution for the nonlinear Dirichlet problem driven by the Finsler–Laplacian competing operator in the Heisenberg group. This solution differs from the concept of the weak solution. To achieve this, we employ a Galerkin type procedure as part of our methodology.