Solutions for nonhomogeneous degenerate quasilinear anisotropic problems

Authors : Abdolrahman Razani, Elisabetta Tornatore

Pages : 134-149

Doi:10.33205/cma.1504337

View : 29 | Download : 36

Publication Date : 2024-09-15

Article Type : Research

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.