## Abstract and Applied Analysis

### Positive Periodic Solutions in Shifts ${\delta }_{{\pm}}$ for a Class of Higher-Dimensional Functional Dynamic Equations with Impulses on Time Scales

#### Abstract

Let $\mathbb{T}\subset \mathbb{R}$ be a periodic time scale in shifts ${\delta }_{{\pm}}$ with period $P\in ({t}_{0},\mathrm{\infty }{)}_{\mathbb{T}}$ and ${t}_{0}\in \mathbb{T}$ is nonnegative and fixed. By using a multiple fixed point theorem in cones, some criteria are established for the existence and multiplicity of positive solutions in shifts ${\delta }_{{\pm}}$ for a class of higher-dimensional functional dynamic equations with impulses on time scales of the following form: ${x}^{\mathrm{\Delta }}(t)=A(t)x(t)+b(t)f(t,x(g(t))), t\ne {t}_{j}, t\in \mathbb{T}, x({t}_{j}^{+})=x({t}_{j}^{-})+{I}_{j}(x({t}_{j})),$ where $A(t)=({a}_{ij}(t){)}_{n{\times}n}$ is a nonsingular matrix with continuous real-valued functions as its elements. Finally, numerical examples are presented to illustrate the feasibility and effectiveness of the results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 509052, 11 pages.

Dates
First available in Project Euclid: 2 October 2014

Hu, Meng; Wang, Lili; Wang, Zhigang. Positive Periodic Solutions in Shifts ${\delta }_{{\pm}}$ for a Class of Higher-Dimensional Functional Dynamic Equations with Impulses on Time Scales. Abstr. Appl. Anal. 2014 (2014), Article ID 509052, 11 pages. doi:10.1155/2014/509052. https://projecteuclid.org/euclid.aaa/1412277064