Multiple positive periodic solutions in shifts &delta;<SUB align="right">± for an impulsive nabla dynamic equation on time scales

Abstract

Abstract:In this paper, based on the theory of calculus on time scales, we first study some properties of the nabla exponential function and shift operators on time scales, then by using a multiple fixed point theorem in cones, sufficient conditions are established for the existence and multiplicity of positive periodic solutions in shifts delta for an impulsive nabla dynamic equation on time scales. Finally, some numerical examples are presented to illustrate the feasibility and effectiveness of the results.