Solutions for nonhomogeneous degenerate quasilinear anisotropic problems

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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