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Existence and controllability results for mixed functional integrodifferential equations with infinite delay

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Abstrakty
EN
Sufficient conditions are established for the existence of solution for mixed neutral functional integrodifferential equations with infinite delay. The results are obtained using the theory of fractional powers of operators and the Sadovskii’s fixed point theorem. As an application we prove a controllability result for the system.
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Strony
893--909
Opis fizyczny
Bibliogr. 24 poz.
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autor
  • Department of Mathematics, Shivaji University, Kolhapur-416 004, Maharashtra, India
Bibliografia
  • [1] C. T. Anh, L. V. Hieu, Existence and uniform asymptotic stability for an abstract differential equation with infinite delay, Electron. J. Differential Equations 51 (2012), 1–14.
  • [2] A. Boufala, H. Bouzahir, Neutral Volterra integrodifferential equations with infinite delay, Int. J. Math. Anal. 3(4) (2009), 187–196.
  • [3] A. Boufala, H. Bouzahir, Local existence for partial neutral functional integrodifferential equations with infinite delay, Commun. Math. Anal. 9(2) (2010), 149–168.
  • [4] H. Bouzahir, X. Fu, Controllability of neutral functional differential equations with infinite delay, Acta Math. Sci. 31B(1) (2011), 73–80.
  • [5] A. Caicedoa, C. Cuevasa, G. M. Mophoub, G. M. N’Guerekata, Asymptotic behavior of solutions of some semilinear functional differential and integro-differential equations with infinite delay in Banach spaces, J. Franklin Inst. 349 (2012), 1–24.
  • [6] J. C. Chang, Existence of some neutral partial differential equations with infinite delay, Nonlinear Anal. 74 (2011), 3204–3217.
  • [7] M. B. Dhakne, K. D. Kucche, Global existence for abstract nonlinear Volterra–Fredholm functional integrodifferential equation, Demonstratio Math. 45(1) (2012), 117–127.
  • [8] M. B. Dhakne, K. D. Kucche, Second order Volterra–Fredholm functional integrodifferential equations, Malaya J. Matematik 1(1) (2012), 1–7.
  • [9] K. J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, Vol. 194, Springer, New York, 2000.
  • [10] K. Ezzinbi, Existence and stability for some partial functional differential equations with infinite, Electron. J. Differential Equations 116 (2003), 1–13.
  • [11] X. Fu, Controllability of neutral functional differential systems in abstract space, Appl. Math. Comput. 141 (2003), 281–296.
  • [12] X. Fu, Existence and stability of solutions to neutral equations with infinite delay, Electron. J. Differential Equations 55 (2013), 1–19.
  • [13] J. Hale, J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), 11–41.
  • [14] E. Hernández, Existence results for partial neutral integrodifferential equations with unbounded delay, J. Math. Anal. Appl. 292(1) (2004), 194–210.
  • [15] E. Hernández, H. R. Henríquez, Existence results for partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl. 221(2) (1998), 452–475.
  • [16] E. Hernández, H. R. Henríquez, Existence of periodic solutions of partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl. 221(2) (1998), 499–522.
  • [17] Y. Hino, S. Murakami, T. Naito, Functional differential equations with infinite delay, Lecture Notes in Math., Vol. 1473, Springer-Verlag, Berlin, 1991.
  • [18] K. D. Kucche, M. B. Dhakne, On existence results and qualitative properties of mild solution of semilinear mixed Volterra–Fredholm functional integrodifferential equations in Banach spaces, Appl. Math. Comput. 219 (2013), 10806–10816.
  • [19] K. D. Kucche, M. B. Dhakne, Controllability results for second order abstract mixed Volterra–Fredholm functional integrodifferential equations, Panamer. Math. J. 22(4) (2012), 109–121.
  • [20] M. Li, Y. Duan, X. Fu, M.Wang, Controllability of neutral functional integrodifferential systems in abstract space, J. Appl. Math. Comput. 23(1–2) (2007), 101–112.
  • [21] C. M. Marle, Mesures et Probabilites, Hermann, Paris, 1974.
  • [22] A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983.
  • [23] M. D. Quinn, N. Carmichael, An approach to nonlinear control problems using fixed point methods, degree theory and pseudo-inverses, Numer. Funct. Anal. Optim. 7 (1984–1985), 197–219.
  • [24] B. N. Sadovskii, On a fixed point principle, Funct. Anal. Appl. 1 (1967), 74–76.
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Bibliografia
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