Existence of Strong and Nontrivial Solutions to Strongly Coupled Elliptic Systems

TL;DR

This paper proves the existence of strong solutions for complex nonlinear strongly coupled elliptic systems with multiple equations, and explores the existence of nontrivial solutions indicating pattern formations.

Contribution

It introduces new results on the existence of strong and nontrivial solutions for multi-equation strongly coupled elliptic systems.

Findings

Existence of strong solutions established

Nontrivial solutions and pattern formations analyzed

Results applicable to systems with more than two equations

Abstract

We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations) will also be studied.