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 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.