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Existence of almost periodic solutions for impulsive neutral functional differential equations. (English) Zbl 1474.34544

Summary: The existence of piecewise almost periodic solutions for impulsive neutral functional differential equations in Banach space is investigated. Our results are based on Krasnoselskii’s fixed-point theorem combined with an exponentially stable strongly continuous operator semigroup. An example is given to illustrate the theory.

MSC:

34K40 Neutral functional-differential equations
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K45 Functional-differential equations with impulses
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[1] Samoilenko, A. M.; Perestyuk, N. A., Impulsive Differential Equations (1995), Singapore: World Scientific, Singapore · Zbl 0837.34003
[2] Stamov, G. T.; Alzabut, J. O.; Atanasov, P.; Stamov, A. G., Almost periodic solutions for an impulsive delay model of price fluctuations in commodity markets, Nonlinear Analysis: Real World Applications, 12, 6, 3170-3176 (2011) · Zbl 1231.34124
[3] Stamov, G. T.; Stamova, I. M., Almost periodic solutions for impulsive neural networks with delay, Applied Mathematical Modelling, 31, 7, 1263-1270 (2007) · Zbl 1136.34332
[4] Alzabut, J. O.; Stamov, G. T.; Sermutlu, E., On almost periodic solutions for an impulsive delay logarithmic population model, Mathematical and Computer Modelling, 51, 5-6, 625-631 (2010) · Zbl 1190.34087
[5] Wang, Q.; Zhang, H.; Ding, M.; Wang, Z., Global attractivity of the almost periodic solution of a delay logistic population model with impulses, Nonlinear Analysis: Theory, Methods & Applications, 73, 12, 3688-3697 (2010) · Zbl 1216.34065
[6] Pan, L.; Cao, J., Anti-periodic solution for delayed cellular neural networks with impulsive effects, Nonlinear Analysis: Real World Applications, 12, 6, 3014-3027 (2011) · Zbl 1231.34121
[7] Cuevas, C.; Hernandez, E.; Rabelo, M., The existence of solutions for impulsive neutral functional differential equations, Computers & Mathematics with Applications. An International Journal, 58, 4, 744-757 (2009) · Zbl 1189.34155
[8] Anguraj, A.; Karthikeyan, K., Existence of solutions for impulsive neutral functional differential equations with nonlocal conditions, Nonlinear Analysis: Theory, Methods & Applications, 70, 7, 2717-2721 (2009) · Zbl 1165.34416
[9] Hernández, E., Global solutions for abstract impulsive neutral differential equations, Mathematical and Computer Modelling, 53, 1-2, 196-204 (2011) · Zbl 1211.34098
[10] Abdelghani, O., Local and global existence and uniqueness results for impulsive functional differential equations with multiple delay, Journal of Mathematical Analysis and Applications, 323, 1, 456-472 (2006) · Zbl 1121.34084
[11] Hernandez, M. E.; Rabello, M.; Henriquez, H. R., Existence of solutions for impulsive partial neutral functional differential equations, Journal of Mathematical Analysis and Applications, 331, 2, 1135-1158 (2007) · Zbl 1123.34062
[12] Chang, Y.; Anguraj, A.; Arjunan, M. M., Existence results for impulsive neutral functional differential equations with infinite delay, Nonlinear Analysis: Hybrid Systems, 2, 1, 209-218 (2008) · Zbl 1170.35467
[13] Ye, R., Existence of solutions for impulsive partial neutral functional differential equation with infinite delay, Nonlinear Analysis: Theory, Methods & Applications A, 73, 1, 155-162 (2010) · Zbl 1198.34177
[14] Hernández, M. E.; Henríquez, H. R.; McKibben, M. A., Existence results for abstract impulsive second-order neutral functional differential equations, Nonlinear Analysis, 70, 7, 2736-2751 (2009) · Zbl 1173.34049
[15] Henríquez, H. R.; de Andrade, B.; Rabelo, M., Existence of almost periodic solutions for a class of abstract impulsive differential equations, ISRN Mathematical Analysis, 2011 (2011) · Zbl 1242.34110
[16] Liu, J. W.; Zhang, C. Y., Existence and stability of almost periodic solutions for impulsive differential equations, Advances in Difference Equations, 34, 14 (2012) · Zbl 1291.34076
[17] 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, 44 (1983), New York, NY. USA: Springer, New York, NY. USA · Zbl 0516.47023
[18] Henríquez, H. R.; Lizama, C., Compact almost automorphic solutions to integral equations with infinite delay, Nonlinear Analysis: Theory, Methods & Applications A, 71, 12, 6029-6037 (2009) · Zbl 1179.43004
[19] Agarwal, R. P.; Cuevas, C.; dos Santos, J. P., Analytic resolvent operator and existence results for fractional integro-differential equations, Journal of Abstract Differential Equations and Applications, 2, 2, 26-47 (2012) · Zbl 1330.45008
[20] Sivasankaran, S.; Arjunan, M. M.; Vijayakumar, V., Existence of global solutions for second order impulsive abstract partial differential equations, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 74, 17, 6747-6757 (2011) · Zbl 1237.34136
[21] Hernandez, E. M.; Aki, S. M. T.; Henríquez, H., Global solutions for impulsive abstract partial differential equations, Computers & Mathematics with Applications, 56, 5, 1206-1215 (2008) · Zbl 1155.35481
[22] Agarwal, R. P.; de Andrade, B.; Cuevas, C., Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 11, 5, 3532-3554 (2010) · Zbl 1248.34004
[23] Chang, Y.; Zhang, R.; N’Guérékata, G. M., Weighted pseudo almost automorphic mild solutions to semilinear fractional differential equations, Computers and Mathematics with Applications, 64, 10, 3160-3170 (2012) · Zbl 1268.34010
[24] Burton, T. A., A fixed-point theorem of Krasnoselskii, Applied Mathematics Letters, 11, 1, 85-88 (1998) · Zbl 1127.47318
[25] Hernández, E.; Henrıquez, H. R., Existence of periodic solutions of partial neutral functional-differential equations with unbounded delay, Journal of Mathematical Analysis and Applications, 221, 2, 499-522 (1998) · Zbl 0926.35151
[26] Diagana, T.; Hernandez, E.; Rabello, M., Pseudo almost periodic solutions to some non-autonomous neutral functional differential equations with unbounded delay, Mathematical and Computer Modelling, 45, 9-10, 1241-1252 (2007) · Zbl 1133.34042
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