Title: Multiple positive periodic solutions in shifts δ_± for an impulsive nabla dynamic equation on time scales

Authors: Meng Hu; Lili Wang

Addresses: School of Mathematics and Statistics, Anyang Normal University, Xian'ge Avenue 436, Anyang, Henan 455000, China ' School of Mathematics and Statistics, Anyang Normal University, Xian'ge Avenue 436, Anyang, Henan 455000, China

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.

Keywords: impulse; nabla dynamic equation; periodic solution; shift operator; time scale.

DOI: 10.1504/IJDSDE.2017.083724

International Journal of Dynamical Systems and Differential Equations, 2017 Vol.7 No.1, pp.1 - 17

Received: 26 May 2016
Accepted: 01 Jul 2016
Published online: 20 Apr 2017 *

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