Abstract and Applied Analysis

Positive Periodic Solutions in Shifts δ ± for a Class of Higher-Dimensional Functional Dynamic Equations with Impulses on Time Scales

Meng Hu, Lili Wang, and Zhigang Wang

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Abstract

Let T R be a periodic time scale in shifts δ ± with period P ( t 0 , ) T and t 0 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 δ ± for a class of higher-dimensional functional dynamic equations with impulses on time scales of the following form: x Δ ( t ) = A ( t ) x ( t ) + b ( t ) f ( t , x ( g ( t ) ) ) ,   t t j ,   t T ,   x ( t j + ) = x ( t j - ) + I j ( x ( t j ) ) , where A ( t ) = ( a i j ( t ) ) n × 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

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277064

Digital Object Identifier
doi:10.1155/2014/509052

Mathematical Reviews number (MathSciNet)
MR3226200

Citation

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


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