Qualitative Results for a First-Order Nonlinear Nabla Dynamic Equation on Time Scales

Abstract

This paper explores the existence of solutions and the stability of first-order nonlinear nabla dynamic equations on time scales. The findings on the existence of solutions are obtained by employing Schauder's fixed point theorem and the technique of lower and upper solutions. Further, the results concerning uniform stability and the Ulam stability of nabla dynamic initial value problems are examined. Moreover, the Gronwall inequality for the nabla derivatives on time scales is reformulated to aid in deriving the above outcomes. We illustrate the findings through suitable examples.