Positive Solution of Singular BVPs for System of Dynamic Equations on Time Scales

TL;DR

This paper establishes necessary and sufficient conditions for positive solutions of a singular second order system of dynamic equations on time scales, using fixed-point theorems and lower/upper solutions methods.

Contribution

It provides new criteria for the existence of positive solutions to singular dynamic systems on time scales, expanding the theoretical framework.

Findings

Derived necessary and sufficient conditions for solutions.

Applied fixed-point theorems and lower/upper solutions methods.

Extended results to singular second order systems on time scales.

Abstract

This paper is devoted to derive some necessary and suficient conditions for the existence of positive solutions to a singular second order system of dynamic equations with Dirichlet boundary conditions. The results are obtained by employing the fixed-point theorems and the method of the lower and upper solutions.