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On Existence of Solutions of Semilinear Impulsive Functional Differential Equations with Nonlocal Conditions

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Recent Advances in Operator Theory, Operator Algebras, and their Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 153))

Abstract

The existence, uniqueness and continuous dependence of a mild solution of a semilinear impulsive functional-differential evolution nonlocal Cauchy problem in general Banach spaces are studied. Methods of fixed point theorems, of a C0 semigroup of operators and the Banach contraction theorem are applied.

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References

  1. H. Akça, A. Boucherif, and V. Covachev, Impulsive Functional-differential Equations with Nonlocal Conditions. Int. J. of Math. and Math. Sci. 29:5 (2002), 251–256.

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  3. L. Byszewski, and H. Akça, Existence of Solutions of a Semilinear Functional-Differential Evolution Nonlocal Problem. Nonlinear Analysis 34:1 (1998), 65–72.

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  4. V. Lakshmikantham, D.D. Bainov, and P.S. Simeonov, Theory of Impulsive Differential Equations. Series in Modern Applied Mathematics, vol. 6, World Scientific, Singapore, 1989.

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  5. A.M. Samoilenko, and N.A. Perestyuk, Impulsive Differential Equations. World Scientific Series on Nonlinear Science. Ser. A: Monographs and Treatises 14, World Scientific, Singapore, 1995.

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Author information

Author notes

  1. Valéry Covachev

    Present address: Department of Mathematics and Statistics College of Science, Sultan Qaboos University, Sultanate of Oman

Authors and Affiliations

  1. Department of Mathematical Science, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Haydar Akça

  2. Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Valéry Covachev

  3. Department of Mathematics, Science College for Girls, Dammam, Saudi Arabia

    Eada Al-Zahrani

Authors
  1. Haydar Akça
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  2. Valéry Covachev
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  3. Eada Al-Zahrani
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of the West Timişoara, Bul. V. Parvan Nr. 4, 1900, Timişoara, Romania

    Dumitru Gaşpar

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest, 70700, Romania

    Dan Timotin

  3. Dipartimento di Matematica, Università di Roma „Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Roma, Italy

    László Zsidó

  4. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Israel Gohberg

  5. Laboratoire AGAT-UMR 8524 U.F.R. de mathématiques, Université des Sciences et Technologie de Lille, 59655, Villeneuve d’Ascq Cedex, France

    Florian-Horia Vasilescu

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© 2004 Birkhäuser Verlag Basel/Switzerland

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Akça, H., Covachev, V., Al-Zahrani, E. (2004). On Existence of Solutions of Semilinear Impulsive Functional Differential Equations with Nonlocal Conditions. In: Gaşpar, D., Timotin, D., Zsidó, L., Gohberg, I., Vasilescu, FH. (eds) Recent Advances in Operator Theory, Operator Algebras, and their Applications. Operator Theory: Advances and Applications, vol 153. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7314-8_1

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