Solutions for nonhomogeneous degenerate quasilinear anisotropic problems

Year 2024, Volume: 7 Issue: 3, 134 - 149, 15.09.2024

Abdolrahman Razani , Elisabetta Tornatore

https://doi.org/10.33205/cma.1504337

Cited By: 1

Abstract

In this article, we consider a class of nonlinear elliptic problems, where anisotropic leading differential operator incorporates the unbounded coefficients and the nonlinear term is a convection term. We prove the solvability of degenerate Dirichlet problem with convection, i.e. the existence of at least one bounded weak solution via the theory of pseudomonotone operators, Nemytskii-type operator and a priori estimate in the degenerate anisotropic Sobolev spaces.

Keywords

Degenerate anisotropic $\vec{p}$-Laplacian, degenerate anisotropic Sobolev spaces, unbounded coefficient, bounded solution, truncation, pseudomonotone operator.

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