Volterra integral equations on time scales: Basic qualitative and quantitative results with applications to initial value problems on unbounded domains

Abstract

This article introduces the basic qualitative and basic quantitative theory of Volterra integral equations on time scales and thus may be considered as a foundation for future advanced studies in the field. New sucient conditions are introduced that guarantee: existence; uniqueness; approximation; boundedness and certain growth rates of solutions to both linear and nonlinear problems. The main techniques employed are contemporary components of nonlinear analysis, including: the fixed‐point theorems