Existence and nonexistence of solutions for p(x)-curl systems arising in electromagnetism

TL;DR

This paper investigates conditions under which solutions exist or do not exist for variable exponent curl systems in electromagnetism, extending previous results from constant exponent cases and addressing a gap in nonexistence findings.

Contribution

It introduces new existence and nonexistence results for p(x)-curl systems, generalizing prior work on p-curl systems and filling a research gap.

Findings

Established conditions for existence of solutions.

Proved nonexistence results for certain p(x)-curl systems.

Extended known results from constant to variable exponent cases.

Abstract

In this paper, we study the existence and the nonexistence of solutions for a new class of $p(x)-$curl systems arising in electromagnetism. This work generalizes some results obtained in the $p-$curl case. There seems to be no results on the nonexistence of solutions for curl systems with variable exponent.