On solvability of a class of nonlinear elliptic type equation with variable exponent

TL;DR

This paper investigates the solvability of a class of nonlinear elliptic equations with variable exponents, providing conditions for solutions without regularization and exploring the properties of the associated operator.

Contribution

It offers new existence results for degenerate nonlinear elliptic equations with variable exponents without restrictions between exponents.

Findings

Established sufficient conditions for solution existence.

Analyzed the properties of the operator domain.

Connected the operator with known functional spaces.

Abstract

In this paper, we study the Dirichlet problem for the implicit degen- erate nonlinear elliptic equation with variable exponent in a bounded domain. We obtain sufficient conditions for the existence of a solution with- out regularization and any restriction between the exponents. Furthermore, we define the domain of the operator generated by posed problem and investigate its some properties and also its relations with known spaces that enable us to prove existence theorem.