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Keywords:
neutral functional differential equation of second order; mild solution; infinite delay; state-dependent delay fixed point; semigroup theory; cosine function
Summary:
Our aim in this work is to provide sufficient conditions for the existence of global solutions of second order neutral functional differential equation with state-dependent delay. We use the semigroup theory and Schauder's fixed point theorem.
References:
[1] Abbas S., Benchohra M.: Advanced Functional Evolution Equations and Inclusions. Springer, Cham, 2015. MR 3381102 | Zbl 1326.34012
[2] Aiello W.G., Freedman H.I., Wu J.: Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM J. Appl. Math. 52 (1992), 855–869. DOI 10.1137/0152048 | MR 1163810
[3] Anguraj A., Arjunan M.M. Hernández E.: Existence results for an impulsive neutral functional differential equation with state-dependent delay. Appl. Anal. 86 (2007), 861–872. DOI 10.1080/00036810701354995 | MR 2355543
[4] Balachandran K., Anthoni S.M.: Existence of solutions of second order neutral functional differential equations. Tamkang J. Math. 30 (1999), 299–309. MR 1729273
[5] Bartha M.: Periodic solutions for differential equations with state-dependent delay and positive feedback. Nonlinear Anal. TMA 53 (2003), 839–857. MR 1971032 | Zbl 1028.34062
[6] Benchohra M., Henderson J., Ntouyas S.K.: Existence results for impulsive multivalued semilinear neutral functional differential inclusions in Banach spaces. J. Math. Anal. Appl. 263 (2001), 763–780. DOI 10.1006/jmaa.2001.7663 | MR 1866239 | Zbl 0998.34064
[7] Benchohra M., Medjadj I.: Global existence results for neutral functional differential equations with state-dependent delay. Differ. Equ. Dyn. Syst., 24 (2016), 189–200. DOI 10.1007/s12591-014-0210-1 | MR 3486011
[8] Benchohra M., Medjadj I., Nieto J.J., Prakash P.: Global existence for functional differential equations with state-dependent delay. J. Funct. Spaces Appl. 2013, Article ID 863561, 7 pages. MR 3132675 | Zbl 1292.34061
[9] Cao Y., Fan J., Gard T.C.: The effects of state-dependent time delay on a stage-structured population growth model. Nonlinear Anal. TMA 19 (1992), 95–105. MR 1174461 | Zbl 0777.92014
[10] Corduneanu C.: Integral Equations and Stability of Feedback Systems. Academic Press, New York, 1973. MR 0358245 | Zbl 0273.45001
[11] Hartung F.: 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. MR 1975850
[12] Domoshnitsky A., Drakhlin M., Litsyn E.: On equations with delay depending on solution. Nonlinear Anal. TMA 49 (2002), 689–701. MR 1894304 | Zbl 1012.34066
[13] Hartung F., Turi J.: Identification of parameters in delay equations with state-dependent lays. Nonlinear Anal. TMA 29 (1997), 1303–1318. MR 1472420
[14] Hartung F., Herdman T.L., Turi J.: Parameter identification in classes of neutral differential equations with state-dependent delays. Nonlinear Anal. TMA 39 (2000), 305–325. MR 1722822 | Zbl 0955.34067
[15] Fattorini H.O.: Second Order Linear Differential Equations in Banach Spaces. North-Holland Mathematics Studies, 108, North-Holland, Amsterdam, 1985. MR 0797071 | Zbl 0564.34063
[16] Granas A., Dugundji J.: Fixed Point Theory. Springer, New York, 2003. MR 1987179 | Zbl 1025.47002
[17] Hale J., Kato J.: Phase space for retarded equations with infinite delay. Funkcial. Ekvac. 21 (1978), 11–41. MR 0492721 | Zbl 0383.34055
[18] Hernández E.: Existence of solutions for a second order abstract functional differential equation with state-dependent delay. Electron. J. Differential Equations 21 (2007), 1–10. Zbl 1113.47061
[19] Hernández E., McKibben M.: On state-dependent delay partial neutral functional differential equations. Appl. Math. Comput. 186 (2007), 294–301. DOI 10.1016/j.amc.2006.07.103 | MR 2316515 | Zbl 1119.35106
[20] Hernández E., Pierri M., Uniáo G.: Existence results for an impulsive abstract partial differential equation with state-dependent delay. Comput. Math. Appl. 52 (2006), 411–420. DOI 10.1016/j.camwa.2006.03.022
[21] Hernández E., Sakthivel R., Tanaka S.: Existence results for impulsive evolution differential equations with state-dependent delay. Electron. J. Differential Equations 28 (2008), 1–11. MR 2390434 | Zbl 1133.35101
[22] Hino Y., Murakami S., Naito T.: Functional Differential Equations with Unbounded Delay. Springer, Berlin, 1991. MR 1122588
[23] Kisynski J.: On cosine operator functions and one parameter group of operators. Studia Math. 49 (1972), 93–105. MR 0312328
[24] Kozak M.: A fundamental solution of a second order differential equation in Banach space. Univ. Iagel. Acta Math. 32 (1995), 275–289. MR 1345144
[25] Li W.-S., Chang Y.-K., Nieto J.J.: Solvability of impulsive neutral evolution differential inclusions with state-dependent delay. Math. Comput. Modelling 49 (2009), 1920–1927. DOI 10.1016/j.mcm.2008.12.010 | MR 2532098
[26] Ntouyas S.K.: Global existence results for certain second order delay integrodifferential equations with nonlocal conditions. Dynam. Systems Appl. 7 (1998), 415–425. MR 1639604 | Zbl 0914.35148
[27] Ntouyas S.K., Tsamatos P.Ch.: Global existence for second order semilinear ordinary and delay integrodifferential equations with nonlocal conditions. Appl. Anal. 67 (1997), 245–257. DOI 10.1080/00036819708840609 | MR 1614061 | Zbl 0906.35110
[28] Rezounenko A.: Partial differential equations with discrete and distributed state-dependent delays. J. Math. Anal. Appl. 326 (2007), 1031–1045. DOI 10.1016/j.jmaa.2006.03.049 | MR 2280961 | Zbl 1178.35370
[29] Rezounenko A., Wu J.: 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. DOI 10.1016/j.cam.2005.01.047 | MR 2209496
[30] Si J.-G., Wang X.P.: Analytic solutions of a second-order functional differential equation with a state dependent delay. Results Math. 39 (2001), 345–352. DOI 10.1007/BF03322694 | MR 1834580
[31] Travis C.C., Webb G.F.: Compactness, regularity, and uniform continuity properties of strongly continuous cosine families. Houston J. Math. 3 (1977), 555–567. MR 0500288 | Zbl 0386.47024
[32] Travis C.C., Webb G.F.: Cosine families and abstract nonlinear second order differential equations. Acta Math. Acad. Sci. Hungar. 32 (1978), 76–96. DOI 10.1007/BF01902205 | MR 0499581 | Zbl 0388.34039
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