Competing Kohn–Spencer Laplacian systems with convection in non-isotropic Folland–Stein space

Here, we study the existence of a generalized and a strong generalized solutions of the Dirichlet competing Kohn–Spencer Laplacian with convection problem {−ΔHnp1u+μ1ΔHnq1u=f1(ξ,u,v,DHnu,DHnv),−ΔHnp2v+μ2ΔHnq2v=f2(ξ,u,v,DHnu,DHnv), on a bounded domain in the non-isotropic Folland–Stein space. Also, we prove the existence of a weak solution. The main tool is Galerkin's method.