Degenerated and Competing Horizontal (p, q)-Laplacians with Weights on the Heisenberg Group. (17th February 2023) - Razani, A.; Figueiredo, Giovany M.
Abstract: In this article, the degenerated horizontal ( p, q )-Laplacian with weights − Δ H, p a ( u ) − Δ H, q b ( u ) = f ( ξ, u, D H u ) and the competing horizontal ( p, q )-Laplacian with weights − Δ H, p a ( u ) + Δ H, q b ( u ) = f ( ξ, u, D H u ) including the Dirchlet boundary condition are studied. The existence and approximation results for these problems are studied where 1 < q < p < ∞, f : Ω × R × H n → R is a Carathéodory function, Ω is a bounded smooth domain in the Heisenberg group H n and Δ H, p stands for the horizontal p -Laplacian on H n . The proofs are based on weighted Heisenberg Sobolev spaces, Nemytskij operators, Browder-Minty Theorem, and finite dimensional approximation.