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Tytuł artykułu

Global Existence and Stability for Neutral Functional Evolution Equations with State-Dependent Delay

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.
Wydawca
Rocznik
Tom
1
Numer
1
Opis fizyczny
Daty
otrzymano
2013-11-22
zaakceptowano
2014-05-12
online
2014-06-30
Twórcy
  • Laboratory of Mathematics, University of Sidi Bel-Abbes, PO Box 89, 22000 Sidi Bel-Abbes, Algeria, adsbaliki@yahoo.fr
  • Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia, benchohra@univ-sba.dz
Bibliografia
  • [1] N.U. Ahmed, Semigroup Theory with Applications to Systems and Control, Pitman Research Notes in Mathematics Series,246. Longman Scientific & Technical, Harlow John Wiley & Sons, Inc. New York, 1991.
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  • [3] S. Baghli and M. Benchohra, Perturbed functional and neutral functional evolution equations with infinite delay in Fréchetspaces, Electron. J. Differential Equations 2008 (69) (2008), 1–19.
  • [4] S. Baghli and M. Benchohra, Global uniqueness results for partial functional and neutral functional evolution equationswith infinite delay, Differential Integral Equations 23 (1&2) (2010), 31–50.
  • [5] S. Baghli and M. Benchohra, Existence results for semilinear neutral functional differential equations involving evolutionoperators in Fréchet spaces, Georgian Math. J. 17 (2010), 1072–9176.
  • [6] A. Caicedo, C. Cuevas, G. M. Mophou, and G. M. N’Guérékata, Asymptotic behavior of solutions of some semilinear functionaldifferential and integro-differential equations with infinite delay in Banach spaces. J. Franklin Inst. 349 (2012), 1-24.[WoS]
  • [7] T. A. Burton and C. Kirk, A fixed point theorem of Krasnoselskii type, Math. Nachrichten 189 (1998), 23–31.
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  • [9] B.C. Dhage, V. Lakshmikantham, On global existence and attractivity results for nonlinear functional integral equations,Nonlinear Anal. 72 (2010), 2219-2227.
  • [10] J. P.C. dos Santos, On state-dependent delay partial neutral functional integro-differential equations, Appl. Math. Comput.216 (2010) 1637–1644.
  • [11] K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New York, 2000.
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  • [13] J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.
  • [14] J. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), 11–41.
  • [15] J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equation, Applied Mathematical Sciences 99,Springer-Verlag, New York, 1993.
  • [16] E. Hernández M. and M. A. McKibben, On state-dependent delay partial neutral functional-differential equations, Appl.Math. Comput. 186 (2007), 294–301.
  • [17] E. Hernández, M. A. McKibben and H. R. Henríquez, Existence results for partial neutral functional differential equationswith state-dependent delay Math. Comput. Modelling 49 (2009), 1260–1267.
  • [18] Y. Hino, S. Murakami, and T. Naito, Functional Differential Equations with Unbounded Delay, Springer-Verlag, Berlin, 1991.
  • [19] V. Kolmanovskii, and A. Myshkis, Introduction to the Theory and Application of Functional-Differential Equations. KluwerAcademic Publishers, Dordrecht, 1999.
  • [20] V. Lakshmikantham, L. Wen and B. Zhang, Theory of Differential Equations with Unbounded Delay, Kluwer Acad. Publ.,Dordrecht, 1994.
  • [21] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York,1983.
  • [22] N. Van Minh, Gaston M. N’Guérékata, and C. Preda. On the asymptotic behavior of the solutions of semilinear nonautonomousequations. Semigroup Forum 87 (2013), 18-34.[WoS]
  • [23] J. Wu, Theory and Application of Partial Functional Differential Equations, Springer-Verlag, New York, 1996.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_msds-2014-0006
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