On the Existence and Uniqueness of Solutions for a Class of Nonlinear Degenerate Elliptic Problems via Browder-Minty Theorem

Abstract

The purpose of this paper is to investigate the existence and uniqueness of weak solutions for a class of nonlinear degenerate elliptic problems of the form: where ν 1 , ν 2 , and ν 3 are A p -weight functions and the operators a , b and g are Carat´eodory functions that satisfy some certain conditions, and φ ∈ L p (cid:48) (Ω , ν 1 − p (cid:48) 1 ) . The approach used for attaining the mentioned purpose is based on the Browder-Minty theorem and the theory of weighted Sobolev spaces.