×

zbMATH — the first resource for mathematics

Existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional-differential equations and applications. (English) Zbl 1123.34060
The authors consider the existence and uniqueness of pseudo almost periodic (mild) solutions to some classes of first-order partial neutral functional-differential equations. Under suitable assumptions, existence and uniqueness results are obtained. Applications include both a partial integro-differential equation arising in control systems and a scalar reaction-diffusion equation with delay.

MSC:
34K30 Functional-differential equations in abstract spaces
35R10 Partial functional-differential equations
45K05 Integro-partial differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Adimy, M.; Ezzinbi, K., Strict solutions of nonlinear hyperbolic neutral differential equations, Appl. math. lett., 12, 1, 107-112, (1999) · Zbl 0941.34075
[2] Ait Dads, E.; Ezzinbi, K., Existence of pseudo almost periodic solution for some abstract semilinear functional differential equation, Dynam. systems appl., 11, 4, 493-498, (2002) · Zbl 1054.34119
[3] Ait Dads, E.; Ezzinbi, K., Pseudo almost periodic solutions of some delay differential equations, J. math. anal. appl., 201, 3, 840-850, (1996) · Zbl 0858.34055
[4] Amir, B.; Maniar, L., Composition of pseudo-almost periodic functions and Cauchy problems with operator of nondense domain, Ann. math. blaise Pascal, 6, 1, 1-11, (1999) · Zbl 0941.34059
[5] Corduneanu, C., Almost periodic functions, (1989), Chelsea New York · Zbl 0672.42008
[6] Cuevas, C.; Pinto, M., Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with nondense domain, Nonlinear anal., 45, 1, 73-83, (2001) · Zbl 0985.34052
[7] Diagana, T., Pseudo almost periodic solutions to some differential equations, Nonlinear anal., 60, 7, 1277-1286, (2005) · Zbl 1061.34040
[8] Diagana, T.; Mahop, C.M.; N’Guérékata, G.M., Pseudo almost periodic solutions to some semilinear differential equations, Math. comput. modelling, 43, 1-2, 89-96, (2006) · Zbl 1096.34038
[9] Fink, A.M., Almost periodic differential equations, Lecture notes in math., vol. 377, (1974), Springer-Verlag New York · Zbl 0325.34039
[10] Hale, J.K.; Verduyn Lunel, S.M., Introduction to functional – differential equations, Appl. math. sci., vol. 99, (1993), Springer-Verlag New York · Zbl 0787.34002
[11] Hale, J.K., Partial neutral functional – differential equations, Rev. roumaine math. pures appl., 39, 4, 339-344, (1994) · Zbl 0817.35119
[12] Hernández, E.; Henríquez, H.R., Existence results for partial neutral functional – differential equations with unbounded delay, J. math. anal. appl., 221, 2, 452-475, (1998) · Zbl 0915.35110
[13] Hernández, E.; Henríquez, H.R., 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
[14] Hernández, E., Existence results for partial neutral integrodifferential equations with unbounded delay, J. math. anal. appl., 292, 1, 194-210, (2004) · Zbl 1056.45012
[15] Hernández, E.M.; Pelicer, M.L., Asymptotically almost periodic and almost periodic solutions for partial neutral differential equations, Appl. math. lett., 18, 11, 1265-1272, (2005) · Zbl 1102.34064
[16] Henríquez, H.R.; Vásquez, C.H., Almost periodic solutions of abstract retarded functional – differential equations with unbounded delay, Acta appl. math., 57, 2, 105-132, (1999) · Zbl 0944.34058
[17] Hino, Y.; Murakami, S., Limiting equations and some stability properties for asymptotically almost periodic functional – differential equations with infinite delay, Tôhoku math. J. (2), 54, 2, 239-257, (2002) · Zbl 1022.34074
[18] Hino, Y.; Murakami, S.; Naito, T., Functional – differential equations with infinite delay, Lecture notes in math., vol. 1473, (1991), Springer-Verlag Berlin · Zbl 0732.34051
[19] Li, H.-X.; Huang, F.-L.; Li, J.-Y., Composition of pseudo almost-periodic functions and semilinear differential equations, J. math. anal. appl., 255, 2, 436-446, (2001) · Zbl 1047.47030
[20] Lunardi, A., Analytic semigroups and optimal regularity in parabolic problems, Pnlde, vol. 16, (1995), Birkhäuser Verlag Basel · Zbl 0816.35001
[21] Minh Man, N.; Van Minh, N., On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations, Commun. pure appl. anal., 3, 2, 291-300, (2004) · Zbl 1083.34053
[22] N’Guérékata, G.M., Topics in almost automorphy, (2005), Springer-Verlag New York · Zbl 1073.43004
[23] Pankov, A.A., Bounded and almost periodic solutions of nonlinear operator differential equations, Math. appl. (Russian series), vol. 55, (1985), Kluwer Academic Publishers, translated from Russian by V.S. Zjackovski and A.A. Pankov · Zbl 0616.34002
[24] Pazy, A., Semigroups of linear operators and applications to partial differential equations, (1983), Springer-Verlag New York · Zbl 0516.47023
[25] Piao, D., Pseudo almost periodic solutions of neutral delay differential equations with piecewise constant arguments, Beijing daxue xuebao ziran kexue ban, 37, 3, 297-304, (2001), (in Chinese) · Zbl 1033.34076
[26] Rankin, S.M., Semilinear evolution equations in Banach spaces with application to parabolic partial differential equations, Trans. amer. math. soc., 336, 2, 523-535, (1993) · Zbl 0785.34044
[27] Yuan, R., Existence of almost periodic solutions of neutral functional – differential equations via liapunov – razumikhin function, Z. angew. math. phys., 49, 1, 113-136, (1998) · Zbl 0895.34056
[28] Yoshizawa, T., Stability theory and the existence of periodic solutions and almost periodic solutions, Appl. math. sci., vol. 14, (1975), Springer-Verlag New York · Zbl 0304.34051
[29] Wu, J.; Xia, H., Rotating waves in neutral partial functional – differential equations, J. dynam. differential equations, 11, 2, 209-238, (1999) · Zbl 0939.35188
[30] 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
[31] Wu, J., Theory and applications of partial functional – differential equations, Appl. math. sci., vol. 119, (1996), Springer-Verlag New York
[32] Zaidman, S., Topics in abstract differential equations, Pitman research notes in mathematics ser. II, (1994-1995), Wiley New York · Zbl 0818.34035
[33] Zaidman, S., Almost-periodic functions in abstract spaces, Res. notes math., vol. 126, (1985), Pitman (Advanced Publishing Program) Boston, MA · Zbl 0648.42006
[34] Zhang, C.Y., Pseudo almost periodic solutions of some differential equations, J. math. anal. appl., 151, 62-76, (1994) · Zbl 0796.34029
[35] Zhang, C.Y., Pseudo almost periodic solutions of some differential equations II, J. math. anal. appl., 192, 543-561, (1995) · Zbl 0826.34040
[36] Zhang, C.Y., Integration of vector-valued pseudo almost periodic functions, Proc. amer. math. soc., 121, 167-174, (1994) · Zbl 0818.42003
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.