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Measure of noncompactness and neutral functional differential equations with state-dependent delay

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Our aim in this work is to study the existence of solutions of first and second order for neutral functional differential equations with state-dependent delay. We use the Mönch’s fixed point theorem for the existence of solutions and the concept of measures of noncompactness.
Rocznik
Tom
Strony
23--45
Opis fizyczny
Bibliogr. 37 poz.
Twórcy
autor
  • Laboratory of Mathematics, University of Sidi Bel-Abbes, PO Box 89, Bel-Abbes 22000, Algeria, benchohra@univ-sba.dz
autor
autor
  • Laboratory of Mathematics, University of Sidi Bel-Abbès, PO Box 89, Bel-Abbès 22000, Algeria, imene.medjadj@hotmail.fr
Bibliografia
  • [1] S. Abbas, M. Benchohra, Advanced Functional Evolution Equations and Inclusions. Springer, Cham, 2015.
  • [2] W.G. Aiello, H.I. Freedman, J. Wu, Analysis of a model representing stage-structured population growth with state-dependent time delay, SIAM J. Appl. Math. 52 (3) (1992) 855-869.
  • [3] R.R. Akhmerov, M.I. Kamenskii, A.S. Patapov, A.E. Rodkina, B.N. Sadovskii, Measures of Noncompactness an Condensing Operators, Birkhauser Verlag, Basel, 1992.
  • [4] J.C. Alvárez, Measure of noncompactness and fixed points of nonexpansive condensing mappings in locally convex spaces, Rev. Real. Acad. Cienc. Exact. Fis. Natur. Madrid 79 (1985) 53-66.
  • [5] A. Anguraj, M.M. Arjunan, E. Hernandez, Existence results for an impulsive neutral functional differential equation with state-dependent delay, Appl. Anal. 86 (2007) 861-872.
  • [6] S. Baghli, M. Benchohra, Global uniqueness results for partial functional and neutral functional evolution equations with infinite delay. Differential Integral Equations 23 (2010) 31-50.
  • [7] K. Balachandran, S. Marshal Anthoni, Existence of solutions of second order neutral functional differential equations, Tamkang J. Math. 30 (1999) 299-309.
  • [8] A. Baliki, M. Benchohra, Global existence and asymptotic behavior for functional evolution equations, J. Appl. Anal. Comput. 4 (2014) 129-138.
  • [9] J. Banas, K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980.
  • [10] M.V. Barbarossa, H.-O. Walther, Linearized, stability for a new class of neutral equations with state-dependent delay, Differ. Equ. Dyn. Syst. 24 (2016) 63-79.
  • [11] M. Bartha, Periodic solutions for differential equations with state-dependent delay and positive feedback, Nonlinear Anal. TMA 53 (6) (2003) 839-857.
  • [12] M. Benchohra, I. Medjadj, Global existence results for functional differential equations with delay Commun. Appl. Anal. 17 (2013) 213-220.
  • [13] Y. Cao, J. Fan, T.C. Gard, The effects of state-dependent time delay on a stage-structured population growth model, Nonlinear Anal. TMA (1992) 95-105.
  • [14] C. Corduneanu, Integral Equations and Stability of Feedback Systems. Academic Press, New York, 1973.
  • [15] A. Domoshnitsky, M. Drakhlin, E. Litsyn, On equations with delay depending on solution, Nonlinear Anal. TMA 49 (2002) 689-701.
  • [16] H.O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, North-Holland Mathematics Studies, Vol. 108, North-Holland, Amsterdam, 1985.
  • [17] D. Guo, V. Lakshmikantham, X. Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer Academic Publishers Group, Dordrecht, 1996.
  • [18] J. Hale, J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978) 11-41.
  • [19] F. Hartung, Parameter estimation by quasilinearization in functional differential equations state-dependent delays: a numerical study. Proceedings of the Third, World Congress of Nonlinear Analysts, Part 7 (Catania, 2000), Nonlinear Anal. TMA 47 (2001) 4557-4566.
  • [20] F. Hartung, J. Turi, Identification of parameters in delay equations with state-dependent lays, Nonlinear Anal. TMA 29 (1997) 1303-1318.
  • [21] F. Hartung, T.L. Herdman, J. Turin, Parameter identification in classes of neutral differential equations with state-dependent delays, Nonlinear Anal. TMA 39 (2000) 305-325.
  • [22] E. Hernandez, Existence of solutions for a second order abstract functional differential equation with state-dependent delay, Electron. J. Differential Equations 21 (2007) 1-10.
  • [23] E. Hernández, M.A. McKibben, On state-dependent delay partial neutral functional-differential equations, Appl. Math. Comput. 186 (2007) 294-301.
  • [24] E. Hernández, A. Prokopczyk, L.A. Ladeira, A note on state-dependent partial functional differential equations with unbounded delay, Nonlinear Anal. RWA 7 (2006) 510-519.
  • [25] E. Hernández, R. Sakthivel, A. Tanaka, Existence results for impulsive evolution differential equations with state-dependent delay, Electron. J. Differential Equations 2008 no. 28 (2008) 1-11.
  • [26] Y. Hino, S. Murakami, T. Naito, Functional Differential Equations with Unbounded Delay, Springer-Verlag, Berlin, 1991.
  • [27] J. Kisyński, On cosine operator functions and one-parameter groups of operators, Studia Math. 44 (1972) 93-105.
  • [28] M. Kozak, A fundamental solution of a second order differential equation in Banach space, Univ. Iagel. Acta Math. 32 (1995) 275-289.
  • [29] H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (1980) 985-999.
  • [30] H. Mönch, G.F. von Harten, On the Cauchy problem for ordinary differential equations in Banach spaces, Archiv. Math. Basel 39 (1982) 153-160.
  • [31] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
  • [32] A. Rezounenko, Partial differential equations with discrete and distributed state-dependent delays, J. Math. Anal. Appl. 326 (2007) 1031-1045.
  • [33] A. Rezounenko, J. Wu, A non-local PDE model for population dynamics with state-selective delay: local theory and global attractors, J. Comput. Appl. Math. 190 (2006) 99-113.
  • [34] J.-G. Si, X.-P. Wang, Analytic solutions of a second-order functional differential equation with a state dependent delay, Results Math. 39 (2001) 345-352.
  • [35] C.C. Travis, G.F. Webb, Compactness, regularity, and uniform continuity properties of strongly continuous cosine families, Houston J. Math. (4) (1977) 555-567.
  • [36] C.C. Travis, G.F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hungar. 32 (1978) 76-96.
  • [37] H.-O. Walther, Merging homoclinic solutions due to state-dependent delay. J. Differential Equations 259 (2015) 473-509.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-de946b4e-35f7-4f1e-99de-e550a2a2ee24
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