Double-Phase Elliptic Equations with Nonlinear Sources Existence and Uniqueness of the Weak Solution

Abstract

In our work, our objective is to prove the existence and uniqueness of a weak solution to a class of nonlinear degenerate elliptic $(p, q)$-Laplacian problem with Dirichlet-type boundary condition by giving $L^ ∞$ data. The principal technique utilized here is the variational method alongside the theory of Orlicz spaces and Minty-Browder theorem.