Differential inclusion systems with double phase competing operators, convection, and mixed boundary conditions

TL;DR

This paper introduces a new framework for analyzing complex differential inclusion systems with double-phase operators, convection, and mixed boundary conditions, using Galerkin's method and multifunction surjectivity.

Contribution

It develops a novel approach to establish existence results for generalized solutions in systems with competing differential operators and complex boundary conditions.

Findings

Established existence of generalized solutions for the systems studied.

Extended the applicability of Galerkin's method to complex inclusion systems.

Provided a new analytical framework for double-phase differential operators.

Abstract

In this paper, a new framework for studying the existence of generalized or strongly generalized solutions to a wide class of inclusion systems involving double-phase, possibly competing differential operators, convection, and mixed boundary conditions is introduced. The technical approach exploits Galerkin's method and a surjective theorem for multifunctions in finite dimensional spaces.