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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 16
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Research Article

Degenerated and competing anisotropic (p,q)-Laplacians with weights

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Pages 4471-4488 | Received 07 Jun 2022, Accepted 16 Aug 2022, Published online: 02 Sep 2022
 

Abstract

Here, the existence and approximation results for degenerated anisotropic (p,q)-Laplacian with weights i=1Nxi((a(x)|uxi|pi2+b(x)|uxi|qi2)uxi)=f(x,u,u)and a competing anisotropic (p,q)-Laplacian with weights i=1Nxi((a(x)|uxi|pi2b(x)|uxi|qi2)uxi)=f(x,u,u)are studied with Dirichlet boundary condition and on a bounded smooth domain in RN, N3 where f:Ω×R×RNR is a Carathéodory function. The proofs are based on weighted antitropic Sobolev spaces, Nemytskij operators and finite dimensional approximation.

2010 Mathematics subject classifications:

Disclosure statement

No potential conflict of interest was reported by the authors.

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