Degenerated and Competing Horizontal (p, q)-Laplacians with Weights on the Heisenberg Group
Abdolrahman Razani, Giovany Malcher Figueiredo · Numerical Functional Analysis and Optimization · 2023
In this article, the degenerated horizontal (p, q)-Laplacian with weights −ΔH,pa(u)−ΔH,qb(u)=f(ξ,u,DHu) and the competing horizontal (p, q)-Laplacian with weights −ΔH,pa(u)+ΔH,qb(u)=f(ξ,u,DHu) including the Dirchlet boundary condition are studied. The existence and approximation results for these problems are studied where 1<q<p<∞, f:Ω×R×Hn→R is a Carathéodory function, Ω is a bounded smooth domain in the Heisenberg group Hn and ΔH,p stands for the horizontal p-Laplacian on Hn. The proofs are based on weighted Heisenberg Sobolev spaces, Nemytskij operators, Browder-Minty Theorem, and finite dimensional approximation.