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2004 | 2 | 4 | 573-583

Tytuł artykułu

On the existence of solutions for nonlinear impulsive periodic viable problems

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
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].

Wydawca

Czasopismo

Rocznik

Tom

2

Numer

4

Strony

573-583

Daty

wydano
2004-08-01
online
2004-08-01

Twórcy

  • University of Perugia
  • University of Rome ‘Tor Vergata’

Bibliografia

  • [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] 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] 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] M. Benchohra, A. Boucherif: “Initial value problems for impulsive differential inclusions of first order”, Diff. Eqns. Dyn. Syst., Vol. 8, (2000), pp. 51–66.
  • [5] M. Benchohra, A. Boucherif: “An existence result for first order initial value problems for impulsive differential inclusions in Banach spaces”, Arch. Math., Vol. 36, (2000), pp. 159–169.
  • [6] M. Benchohra, A. Boucherif, J.J. Nieto: “On initial value problems for a class of first order impulsive differential inclusions”, Disc. Math. Diff. Incl. Control Optim., Vol. 21, (2001), pp. 159–171.
  • [7] M. Benchohra, J. Henderson, S.K. Ntouyas: “On a periodic boundary value problem for first order impulsive differential inclusions”, Dyn. Syst. Appl., Vol. 10, (2001), pp. 477–488.
  • [8] M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahabi: “Existence results for impulsive lower semicontinuous differential inclusions”, Int. J. Pure Appl. Math., Vol. 1, (2002), pp. 431–443.
  • [9] M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahabi: “Existence results for impulsive functional and neutral functional differential inclusions with lower semicontinuous right hand side”, Electron. J. Math. Phys. Sci., Vol. 1, (2002), pp. 72–91.
  • [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
  • [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.
  • [12] M. Frigon, D. O’Regan: “Existence results for first order impulsive differential equations”, J. Math. Anal. Appl., Vol. 193, (1995), pp. 96–113. http://dx.doi.org/10.1006/jmaa.1995.1224
  • [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] S. Hu, N.S. Papageorgiou: Handbook of multivalued analysis, Kluwer, Dordrecht, The Netherlands, 1997.
  • [15] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov: Theory of impulsive differential equations, World Scientific, Singapore, 1989.
  • [16] V.D. Mil’man, A.D. Myshkis: “On the stability of motion in the presence of impulses”, Siberian Math. J., Vol. 1, (1960), pp. 233–237.
  • [17] A.M. Samoilenko, N.A. Perestyuk: “Differential equations with impulse effect”, Visca Skola, Kiev, 1987. [in Russian]
  • [18] P.J. Watson: “Impulsive differential inclusions”, Nonlin. World, Vol. 4, (1997), pp. 395–402.

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bwmeta1.element.doi-10_2478_BF02475964