Non-potential systems with relativistic operators and maximal monotone boundary conditions

TL;DR

This paper investigates the solvability of a non-potential system involving relativistic operators with boundary conditions defined by maximal monotone operators, using fixed point methods and a priori estimates.

Contribution

It introduces a novel approach combining fixed point formulation with a priori estimates for systems with relativistic operators and maximal monotone boundary conditions.

Findings

Established conditions for solvability of the system.

Developed a fixed point framework for the analysis.

Provided a priori estimates ensuring convergence.

Abstract

We are concerned with solvability of a non-potential system involving two relativistic operators, subject to boundary conditions expressed in terms of maximal monotone operators. The approach makes use of a fixed point formulation and relies on a priori estimates and convergent to zero matrices.