APPROXIMATE CONTROLLABILITY OF SECOND ORDER IMPULSIVE FUNCTIONAL DIFFERENTIAL SYSTEM WITH INFINITE DELAY IN BANACH SPACES

Meili Li; Junling Ma

doi:10.11948/2016036

2016 Volume 6 Issue 2

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Meili Li, Junling Ma. APPROXIMATE CONTROLLABILITY OF SECOND ORDER IMPULSIVE FUNCTIONAL DIFFERENTIAL SYSTEM WITH INFINITE DELAY IN BANACH SPACES[J]. Journal of Applied Analysis & Computation, 2016, 6(2): 492-514. doi: 10.11948/2016036

Citation:

Meili Li, Junling Ma. APPROXIMATE CONTROLLABILITY OF SECOND ORDER IMPULSIVE FUNCTIONAL DIFFERENTIAL SYSTEM WITH INFINITE DELAY IN BANACH SPACES[J]. Journal of Applied Analysis & Computation, 2016, 6(2): 492-514. doi: 10.11948/2016036

APPROXIMATE CONTROLLABILITY OF SECOND ORDER IMPULSIVE FUNCTIONAL DIFFERENTIAL SYSTEM WITH INFINITE DELAY IN BANACH SPACES

Meili Li^1,2,
Junling Ma²

1 School of Science, Donghua University, Shanghai, China 201620;
2 Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 2Y2

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Abstract

Abstract

This paper studies the approximate controllability of second order impulsive functional differential system with infinite delay in Banach spaces. Sufficient conditions are formulated and proved for the approximate controllability of such system under the assumption that the associated linear part of system is approximately controllable. The results are obtained by using strongly continuous cosine families of operators and the contraction mapping principle. An example is given to illustrate the obtained theory.
- Approximate controllability /
- strongly continuous cosine families of operators /
- impulsive functional differential system /
- infinite delay
MSC: 93B05;34G20

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References

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