Have a personal or library account? Click to login
Necessary and sufficient conditions for uniform stability of Volterra integro-dynamic equations using new resolvent equation Cover

Necessary and sufficient conditions for uniform stability of Volterra integro-dynamic equations using new resolvent equation

Open Access
|Mar 2014

References

  1. [1] Adivar, M., Principal matrix solutions and variation of parameters for Volterra integro-dynamic equations on time scales, Glasg. Math. J. 53 (2011) 463-480.10.1017/S0017089511000073
  2. [2] Adivar, M. and Raffoul, Y. N., Existence of resolvent for Volterra integral equations on time scales, Bull. of Aust. Math. Soc., 82(1), (2010), 139­155.10.1017/S0004972709001166
  3. [3] Adivar, M. and Raffoul, Y. N., Existence results for periodic solutions of integro-dynamic equations on time scales, Ann. Mat. Pura Appl., 188 (4), 2009, 543-559.10.1007/s10231-008-0088-z
  4. [4] Adivar, M., Function bounds for solutions of Volterra integro-dynamic equations on time scales, Electron. J. Qual. Theory Differ. Equ., No. 7. (2010), pp. 1-22.
  5. [5] Akin-Bohner, E. and Raffoul Y. N., Boundedness in functional dynamic equations on time scales, Adv. Difference Equ., Volume 2006, Art. ID 79689, Pages 1-18.10.1155/ADE/2006/79689
  6. [6] Bohner, M. and Peterson, A., Dynamic Equations on Time Scales, An in­troduction with applications. Birkhauser Boston Inc., Boston, MA, 2001.10.1007/978-1-4612-0201-1
  7. [7] Bohner, M. and Peterson, A., Advances in Dynamic Equations on Time Scales, Birkhauser Boston Inc., Boston, MA, 2003.10.1007/978-0-8176-8230-9
  8. [8] Eloe, P., Islam, M., and Zhang, B., Uniform asymptotic stability in linear Volterra integro-differential equations with applications to delay systems, Dynam. Systems Appl., 9 (2000), 331-344.
  9. [9] Khandaker T. M., Raffoul Y. N, Stability properties of linear Volterra discrete systems with nonlinear perturbation, J. Difference Equ. Appl. 8 (2002), no. 10, 857-874.
  10. [10] Kulik, T. and Tisdell, C. C., Volterra integral equations on time scales: Basic qualitative and quantitative results with applications to initial value problems on unbounded domains. Int. J. Difference Equ. 3 (2008), no. 1, 103-133.
  11. [11] Miller, R. K., Asymptotic stability properties of Volterra integro- differential systems, J. Differential Equations, 10(1971), 485-50610.1016/0022-0396(71)90008-8
  12. [12] Miller, R. K., Nonlinear Volterra integral equations. W. A. Benjamin, Inc., Menlo Park, Calif., 1971.
  13. [13] Tisdell, C. C. and Zaidi, A., Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an appli­cation to economic modelling. Nonlinear Anal., Vol. 68(2008), No. 11,. 3504-3524.
DOI: https://doi.org/10.2478/auom-2013-0039 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 17 - 32
Published on: Mar 5, 2014
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2014 Murat Advar, Youssef N. Raffoul, published by Ovidius University of Constanta
This work is licensed under the Creative Commons License.