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

Abstract

Here, we study the existence of a generalized and a strong generalized solutions of the Dirichlet competing Kohn–Spencer Laplacian with convection problem { − Δ H n p 1 u + μ 1 Δ H n q 1 u = f 1 ( ξ , u , v , D H n u , D H n v ) , − Δ H n p 2 v + μ 2 Δ H n q 2 v = f 2 ( ξ , u , v , D H n u , D H n v ) , 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.