Positive Periodic Solutions in Shifts δ± for a Class of Higher-Dimensional Functional Dynamic Equations with Impulses on Time Scales
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 dy...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/509052 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |