On the existence of solutions for nonlinear impulsive periodic viable problems

Tiziana Cardinali; Raffaella Servadei

Open Mathematics (2004)

  • Volume: 2, Issue: 4, page 573-583
  • ISSN: 2391-5455

Abstract

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In this paper we prove the existence of periodic solutions for nonlinear impulsive viable problems monitored by differential inclusions of the type x′(t)∈F(t,x(t))+G(t,x(t)). Our existence theorems extend, in a broad sense, some propositions proved in [10] and improve a result due to Hristova-Bainov in [13].

How to cite

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Tiziana Cardinali, and Raffaella Servadei. "On the existence of solutions for nonlinear impulsive periodic viable problems." Open Mathematics 2.4 (2004): 573-583. <http://eudml.org/doc/268906>.

@article{TizianaCardinali2004,
abstract = {In this paper we prove the existence of periodic solutions for nonlinear impulsive viable problems monitored by differential inclusions of the type x′(t)∈F(t,x(t))+G(t,x(t)). Our existence theorems extend, in a broad sense, some propositions proved in [10] and improve a result due to Hristova-Bainov in [13].},
author = {Tiziana Cardinali, Raffaella Servadei},
journal = {Open Mathematics},
keywords = {34A37; 34A60; 34B15},
language = {eng},
number = {4},
pages = {573-583},
title = {On the existence of solutions for nonlinear impulsive periodic viable problems},
url = {http://eudml.org/doc/268906},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Tiziana Cardinali
AU - Raffaella Servadei
TI - On the existence of solutions for nonlinear impulsive periodic viable problems
JO - Open Mathematics
PY - 2004
VL - 2
IS - 4
SP - 573
EP - 583
AB - In this paper we prove the existence of periodic solutions for nonlinear impulsive viable problems monitored by differential inclusions of the type x′(t)∈F(t,x(t))+G(t,x(t)). Our existence theorems extend, in a broad sense, some propositions proved in [10] and improve a result due to Hristova-Bainov in [13].
LA - eng
KW - 34A37; 34A60; 34B15
UR - http://eudml.org/doc/268906
ER -

References

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  1. [1] D.D. Bainov, V. Covachev: Impulsive differential equations with a small parameter, World Scientific, Series on Advances in Math. for Applied sciences, 1994. 
  2. [2] D.D. Bainov, P.S. Simeonov: Systems with impulsive effect. Stability, theory and applications, Ellis Horwood Series in Maths and Appl., Ellis Horwood, Chicester, 1989. 
  3. [3] D.D. Bainov, P.S. Simeonov: Impulsive differential equations. Asymptotic properties of the solutions, World Scientific, Series on Advances in Math. for Applied Sciences, 1995. 
  4. [4] M. Benchohra, A. Boucherif: “Initial value problems for impulsive differential inclusions of first order”, Diff. Eqns. Dyn. Syst., Vol. 8, (2000), pp. 51–66. Zbl0988.34005
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  10. [10] T. Cardinali, R. Servadei: “Periodic solutions of nonlinear impulsive differential inclusions with constraints”, Proc. AMS, Vol. 132, (2004), pp. 2339–2349. http://dx.doi.org/10.1090/S0002-9939-04-07343-5 Zbl1069.34004
  11. [11] B.C. Dhage, A. Boucherif, S.K. Ntouyas: “On periodic boundary value problems of first-order perturbed impulsive differential inclusions”, Electron. J. Diff. Eqns., Vol. 84, (2004), pp. 1–9. Zbl1062.34008
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  13. [13] S.G. Hristova, D.D. Bainov: “Existence of periodic solutions of nonlinear systems of differential equations with impulse effect”, J. Math. Anal. Appl., Vol. 125, (1987), pp. 192–202. http://dx.doi.org/10.1016/0022-247X(87)90174-0 
  14. [14] S. Hu, N.S. Papageorgiou: Handbook of multivalued analysis, Kluwer, Dordrecht, The Netherlands, 1997. Zbl0887.47001
  15. [15] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov: Theory of impulsive differential equations, World Scientific, Singapore, 1989. 
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  18. [18] P.J. Watson: “Impulsive differential inclusions”, Nonlin. World, Vol. 4, (1997), pp. 395–402. Zbl0944.34007

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