Existence results for abstract neutral functional differential equations

Hernández, Eduardo; O’Regan, Donal

doi:10.1090/S0002-9939-09-09934-1

Existence results for abstract neutral functional differential equations
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by Eduardo Hernández and Donal O’Regan PDF

Proc. Amer. Math. Soc. 137 (2009), 3309-3318 Request permission

Abstract:

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.

References

Mostafa Adimy and Khalil Ezzinbi, A class of linear partial neutral functional-differential equations with nondense domain, J. Differential Equations 147 (1998), no. 2, 285–332. MR 1633941, DOI 10.1006/jdeq.1998.3446
K. Balachandran, G. Shija, and J. H. Kim, Existence of solutions of nonlinear abstract neutral integrodifferential equations, Comput. Math. Appl. 48 (2004), no. 10-11, 1403–1414. MR 2107098, DOI 10.1016/j.camwa.2004.08.002
K. Balachandran and R. Sakthivel, Existence of solutions of neutral functional integrodifferential equation in Banach spaces, Proc. Indian Acad. Sci. Math. Sci. 109 (1999), no. 3, 325–332. MR 1709339, DOI 10.1007/BF02843536
M. Benchohra and S. K. Ntouyas, Nonlocal Cauchy problems for neutral functional differential and integrodifferential inclusions in Banach spaces, J. Math. Anal. Appl. 258 (2001), no. 2, 573–590. MR 1835560, DOI 10.1006/jmaa.2000.7394
M. Benchohra, J. Henderson, and S. K. Ntouyas, Existence results for impulsive multivalued semilinear neutral functional differential inclusions in Banach spaces, J. Math. Anal. Appl. 263 (2001), no. 2, 763–780. MR 1866239, DOI 10.1006/jmaa.2001.7663
J. P. Dauer and K. Balachandran, Existence of solutions of nonlinear neutral integrodifferential equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), no. 1, 93–105. MR 1790400, DOI 10.1006/jmaa.2000.7022
Piermarco Cannarsa and Daniela Sforza, Global solutions of abstract semilinear parabolic equations with memory terms, NoDEA Nonlinear Differential Equations Appl. 10 (2003), no. 4, 399–430. MR 2016932, DOI 10.1007/s00030-003-1004-2
Ph. Clément and J. A. Nohel, Asymptotic behavior of solutions of nonlinear Volterra equations with completely positive kernels, SIAM J. Math. Anal. 12 (1981), no. 4, 514–535. MR 617711, DOI 10.1137/0512045
Philippe Clément and Jan Prüss, Global existence for a semilinear parabolic Volterra equation, Math. Z. 209 (1992), no. 1, 17–26. MR 1143209, DOI 10.1007/BF02570816
Richard Datko, Linear autonomous neutral differential equations in a Banach space, J. Differential Equations 25 (1977), no. 2, 258–274. MR 447743, DOI 10.1016/0022-0396(77)90204-2
Hui Fang and Jibin Li, On the existence of periodic solutions of a neutral delay model of single-species population growth, J. Math. Anal. Appl. 259 (2001), no. 1, 8–17. MR 1836440, DOI 10.1006/jmaa.2000.7340
H. I. Freedman and Yang Kuang, Some global qualitative analyses of a single species neutral delay differential population model, Rocky Mountain J. Math. 25 (1995), no. 1, 201–215. Second Geoffrey J. Butler Memorial Conference in Differential Equations and Mathematical Biology (Edmonton, AB, 1992). MR 1340003, DOI 10.1216/rmjm/1181072278
Andrzej Granas and James Dugundji, Fixed point theory, Springer Monographs in Mathematics, Springer-Verlag, New York, 2003. MR 1987179, DOI 10.1007/978-0-387-21593-8
Morton E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal. 31 (1968), no. 2, 113–126. MR 1553521, DOI 10.1007/BF00281373
Jack K. Hale and Sjoerd M. Verduyn Lunel, Introduction to functional-differential equations, Applied Mathematical Sciences, vol. 99, Springer-Verlag, New York, 1993. MR 1243878, DOI 10.1007/978-1-4612-4342-7
Jack K. Hale, Partial neutral functional-differential equations, Rev. Roumaine Math. Pures Appl. 39 (1994), no. 4, 339–344. MR 1317773
Eduardo Hernández and Hernán R. Henríquez, Existence results for partial neutral functional-differential equations with unbounded delay, J. Math. Anal. Appl. 221 (1998), no. 2, 452–475. MR 1621730, DOI 10.1006/jmaa.1997.5875
Eduardo Hernández, Existence results for partial neutral functional integrodifferential equations with unbounded delay, J. Math. Anal. Appl. 292 (2004), no. 1, 194–210. MR 2050224, DOI 10.1016/j.jmaa.2003.11.052
Hernán R. Henríquez, Regularity of solutions of abstract retarded functional-differential equations with unbounded delay, Nonlinear Anal. 28 (1997), no. 3, 513–531. MR 1420796, DOI 10.1016/0362-546X(95)00160-W
Yang Kuang, Qualitative analysis of one- or two-species neutral delay population models, SIAM J. Math. Anal. 23 (1992), no. 1, 181–200. MR 1145167, DOI 10.1137/0523009
Qiong Li, Jinde Cao, and Shidong Wan, Positive periodic solution for a neutral delay model in population, J. Biomath. 13 (1998), no. 4, 435–438. MR 1685124
Alessandra Lunardi, On the linear heat equation with fading memory, SIAM J. Math. Anal. 21 (1990), no. 5, 1213–1224. MR 1062400, DOI 10.1137/0521066
Jace W. Nunziato, On heat conduction in materials with memory, Quart. Appl. Math. 29 (1971), 187–204. MR 295683, DOI 10.1090/S0033-569X-1971-0295683-6
A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486, DOI 10.1007/978-1-4612-5561-1
Jianhong Wu and Huaxing Xia, Self-sustained oscillations in a ring array of coupled lossless transmission lines, J. Differential Equations 124 (1996), no. 1, 247–278. MR 1368068, DOI 10.1006/jdeq.1996.0009