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

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: Let T⊂R be a periodic time scale in shifts δ± with period P∈(t0,∞) T and t0∈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: xΔ(t)=A(t)x(t)+b(t)f(t,x(g(t))), t≠tj, t∈T, x(tj+)=x(tj-)+Ij(x(tj)), where A(t) = (aij(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.

Date: 2014
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https://doi.org/10.1155/2014/509052

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:509052

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