Degenerated and competing anisotropic ( <i>p,q</i> )-Laplacians with weights

Abstract

Here, the existence and approximation results for degenerated anisotropic (p,q)-Laplacian with weights −∑i=1N∂∂xi((a(x)|∂u∂xi|pi−2+b(x)|∂u∂xi|qi−2)∂u∂xi)=f(x,u,∇u)and a competing anisotropic (p,q)-Laplacian with weights −∑i=1N∂∂xi((a(x)|∂u∂xi|pi−2−b(x)|∂u∂xi|qi−2)∂u∂xi)=f(x,u,∇u)are studied with Dirichlet boundary condition and on a bounded smooth domain in RN, N≥3 where f:Ω×R×RN→R is a Carathéodory function. The proofs are based on weighted antitropic Sobolev spaces, Nemytskij operators and finite dimensional approximation.

Topics & Concepts