×

Existence results for partial neutral functional differential equations with state-dependent delay. (English) Zbl 1165.34420

Summary: We study the existence of mild solutions for a class of first order abstract partial neutral differential equations with state-dependent delay.

MSC:

34K30 Functional-differential equations in abstract spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hartung, Ferenc; Krisztin, Tibor; Walther, Hans-Otto; Wu, Jianhong, (Functional Differential Equations with State-Dependent Delays: Theory and Applications. Functional Differential Equations with State-Dependent Delays: Theory and Applications, Handbook of Differential Equations: Ordinary Differential Equations, vol. 3 (2006)), 435-545
[2] Arino, Ovide; Boushaba, Khalid; Khalid, Boussouar, Ahmed A mathematical model of the dynamics of the phytoplankton-nutrient system. Spatial heterogeneity in ecological models (Alcalá de Henares, 1998), Nonlinear Anal. RWA, 1, 1, 69-87 (2000) · Zbl 0984.92032
[3] Aiello, Walter; Freedman, H. I.; Wu, Jianhong, Analysis of a model representing stage-structured population growth with state-dependent time delay, SIAM J. Appl. Math., 52, 3, 855-869 (1992) · Zbl 0760.92018
[4] Bartha, Maria, Periodic solutions for differential equations with state-dependent delay and positive feedback, Nonlinear Anal. TMA, 53, 6, 839-857 (2003) · Zbl 1028.34062
[5] Cao, Yulin; Fan, Jiangping; Gard, Thomas, The effects of state-dependent time delay on a stage-structured population growth model, Nonlinear Analysis TMA, 19, 2, 95-105 (1992) · Zbl 0777.92014
[6] Domoshnitsky, Alexander; Drakhlin, Michael; Litsyn, Elena, On equations with delay depending on solution, Nonlinear Analysis TMA, 49, 5, 689-701 (2002) · Zbl 1012.34066
[7] Hartung, Ferenc, Linearized stability in periodic functional differential equations with state-dependent delays, J. Comput. Appl. Math., 174, 2, 201-211 (2005) · Zbl 1077.34074
[8] Hartung, Ferenc, Parameter estimation by quasilinearization in functional differential equations with state-dependent delays: A numerical study, Proceedings of the Third World Congress of Nonlinear Analysis, Part 7 (Catania, 2000). Proceedings of the Third World Congress of Nonlinear Analysis, Part 7 (Catania, 2000), Nonlinear Analysis TMA, 47, 7, 4557-4566 (2001) · Zbl 1042.34582
[9] Hartung, Ferenc; Herdman, Terry L.; Turi, Janos, Parameter identification in classes of neutral differential equations with state-dependent delays, Nonlinear Analysis TMA. Ser. A: Theory Methods, 39, 3, 305-325 (2000) · Zbl 0955.34067
[10] Hartung, Ferenc; Turi, Janos, Identification of parameters in delay equations with state-dependent delays, Nonlinear Analysis TMA, 29, 11, 1303-1318 (1997) · Zbl 0894.34071
[11] Kuang, Y.; Smith, H. L., Slowly oscillating periodic solutions of autonomous state-dependent delay equations, Nonlinear Analysis TMA, 19, 9, 855-872 (1992) · Zbl 0774.34054
[12] Yang, Zhihui; Cao, Jinde, Periodic solutions for general nonlinear state-dependent delay logistic equations, Nonlinear Anal., 66, 6, 1378-1387 (2007) · Zbl 1119.34051
[13] Driver, R. D., A neutral system with state-dependent delay, J. Differential Equations, 54, 1, 73-86 (1984) · Zbl 0543.34053
[14] Hartung, Ferenc; Herdman, Terry L.; Turi, Janos, On existence, uniqueness and numerical approximation for neutral equations with state-dependent delays. Volterra centennial (Tempe, AZ, 1996), Appl. Numer. Math., 24, 2-3, 393-409 (1997) · Zbl 0939.65101
[15] Yang, Zhihui; Cao, Jinde, Existence of periodic solutions in neutral state-dependent delays equations and models, J. Comput. Appl. Math., 174, 1, 179-199 (2005) · Zbl 1107.34059
[16] Hernández, Eduardo; Prokopczyk, Andréa; Ladeira, Luiz, A note on partial functional differential equations with state-dependent delay, Nonlinear Anal. RWA, 7, 4, 510-519 (2006) · Zbl 1109.34060
[17] Rezounenko, Alexander V.; Wu, Jianhong, A non-local PDE model for population dynamics with state-selective delay: Local theory and global attractors, J. Comput. Appl. Math., 190, 1-2, 99-113 (2006) · Zbl 1082.92039
[18] Hale, J. K.; Lunel, Verduyn, (Introduction to Functional-Differential Equations. Introduction to Functional-Differential Equations, Appl. Math. Sci., vol. 99 (1993), Springer-Verlag: Springer-Verlag New York) · Zbl 0787.34002
[19] Adimy, M.; Ezzinbi, K., A class of linear partial neutral functional-differential equations with nondense domain, J. Differential Equations, 147, 2, 285-332 (1998) · Zbl 0915.35109
[20] Hale, Jack, Partial neutral functional differential equations, Rev. Roumaine Math. Pures Appl., 39, 4, 339-344 (1994) · Zbl 0817.35119
[21] Wu, Jianhong, (Theory and Applications of Partial Functional-Differential Equations. Theory and Applications of Partial Functional-Differential Equations, Applied Mathematical Sciences, vol. 119 (1996), Springer-Verlag: Springer-Verlag New York) · Zbl 0870.35116
[22] Wu, J.; Xia, H., Rotating waves in neutral partial functional-differential equations, J. Dynam. Differential Equations, 11, 2, 209-238 (1999) · Zbl 0939.35188
[23] Wu, J.; Xia, H., Self-sustained oscillations in a ring array of coupled lossless transmission lines, J. Differential Equations, 124, 1, 247-278 (1996) · Zbl 0840.34080
[24] Hernández, E.; Henríquez, H., Existence results for partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl., 221, 2, 452-475 (1998) · Zbl 0915.35110
[25] Hernández, E.; Henríquez, H., Existence of periodic solutions of partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl., 221, 2, 499-522 (1998) · Zbl 0926.35151
[26] Hernández, E., Existence results for partial neutral integrodifferential equations with unbounded delay, J. Math. Anal. Appl., 292, 1, 194-210 (2004) · Zbl 1056.45012
[27] Pazy, A., (Semigroups of Linear Operators and Applications to Partial Differential Equations. Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, vol. 44 (1983), Springer-Verlag: Springer-Verlag New York, Berlin) · Zbl 0516.47023
[28] Hino, Yoshiyuki; Murakami, Satoru; Naito, Toshiki, (Functional Differential Equations with Infinite Delay. Functional Differential Equations with Infinite Delay, Lecture Notes in Mathematics, vol. 1473 (1991), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0732.34051
[29] Granas, A.; Dugundji, J., Fixed Point Theory (2003), Springer-Verlag: Springer-Verlag New York · Zbl 1025.47002
[30] Lunardi, A., (Analytic Semigroups and Optimal Regularity in Parabolic Problems. Analytic Semigroups and Optimal Regularity in Parabolic Problems, PNLDE, vol. 16 (1995), Birkhauser Verlag: Birkhauser Verlag Basel) · Zbl 0816.35001
[31] Martin, R. H., Nonlinear Operators and Differential Equations in Banach Spaces (1987), Robert E. Krieger Publ. Co.: Robert E. Krieger Publ. Co. Florida
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.