Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Czasopismo
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
autor
- Department of Mathematics, Baylor University, Waco, Texas 76798-7328 USA
autor
- Laboratory of Mathematics, University of Sidi Bel-Abbès, PO Box 89, Bel-Abbès 22000, Algeria
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