A non-variational approach to the existence of nonzero positive solutions for elliptic systems

TL;DR

This paper introduces a novel non-variational method combining iterative techniques and fixed point index to establish the existence of positive solutions for elliptic systems, supported by illustrative examples.

Contribution

It presents a new approach that does not rely on variational methods to prove positive solutions for elliptic systems.

Findings

Established existence of positive solutions under new conditions

Demonstrated the effectiveness of combined iterative and fixed point methods

Provided examples illustrating theoretical results

Abstract

We provide new results on the existence of nonzero positive weak solutions for a class of second order elliptic systems. Our approach relies on a combined use of iterative techniques and classical fixed point index. Some examples are presented to illustrate the theoretical results.