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ON PSEUDO $ \mathcal{S} $ -ASYMPTOTICALLY PERIODIC FUNCTIONS

  • MICHELLE PIERRI (a1) and VANESSA ROLNIK (a2)
Abstract

We introduce the concept of pseudo $ \mathcal{S} $ -asymptotically periodic functions and study some of the qualitative properties of functions of this type. In addition, we discuss the existence of pseudo $ \mathcal{S} $ -asymptotically periodic mild solutions for abstract neutral functional differential equations. Some applications involving ordinary and partial differential equations with delay are presented.

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Corresponding author
michellepierri@ffclrp.usp
References
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[1]de Andrade, B. and Cuevas, C., ‘-asymptotically -periodic and asymptotically -periodic solutions to semilinear Cauchy problems with non dense domain’, Nonlinear Anal. 72 (2010), 31903208.
[2]Corduneanu, C., Almost Periodic Functions, 2nd edn (Chelsea, New York, 1989).
[3]Cuevas, C. and Lizama, C., ‘-asymptotically -periodic solutions for semilinear Volterra equations’, Math. Methods Appl. Sci. 33 (13) (2010), 16281636.
[4]Cuevas, C. and de Souza, J. C., ‘-asymptotically -periodic solutions of semilinear fractional integro-differential equations’, Appl. Math. Lett. 22 (6) (2009), 865870.
[5]Cuevas, C. and de Souza, J. C., ‘Existence of -asymptotically -periodic solutions for fractional order functional integro-differential equations with infinite delay’, Nonlinear Anal. 72 (3–4) (2010), 16831689.
[6]Chukwu, E. N., Differential Models and Neutral Systems for Controlling the Wealth of Nations, Series on Advances in Mathematics for Applied Sciences, 54 (World Scientific, River Edge, NJ, 2001).
[7]Gurtin, M. E. and Pipkin, A. C., ‘A general theory of heat conduction with finite wave speed’, Arch. Rat. Mech. Anal. 31 (1968), 113126.
[8]Henríquez, H., Pierri, M. and Táboas, P., ‘Existence of -asymptotically -periodic solutions for abstract neutral equations’, Bull. Aust. Math. Soc. 78 (3) (2008), 365382.
[9]Henríquez, H., Pierri, M. and Táboas, P., ‘On -asymptotically -periodic functions on Banach spaces and applications’, J. Math. Anal. Appl. 343 (2) (2008), 11191130.
[10]Hernández, E., ‘Existence results for partial neutral integro-differential equations with unbounded delay’, J. Math. Anal. Appl. 292 (1) (2004), 194210.
[11]Hernández, E. and Henríquez, H., ‘Existence results for partial neutral functional differential equation with unbounded delay’, J. Math. Anal. Appl. 221 (2) (1998), 452475.
[12]Hernández, E. and O’Regan., D., ‘-Hölder classical solutions for non-autonomous neutral differential equations’, Discrete Contin. Dyn. Syst. A 29 (1) (2011), 241260.
[13]Hernández, E. and O’Regan, D., ‘On a new class of abstract neutral differential equations’, J. Funct. Anal. 261 (12) (2011), 34573481.
[14]Levitan, B. M. and Zhikov, V. V., Almost Periodic Functions and Differential Equations (Cambridge University Press, Cambridge, 1982).
[15]Liang, Z. C., ‘Asymptotically periodic solutions of a class of second order nonlinear differential equations’, Proc. Amer. Math. Soc. 99 (4) (1987), 693699.
[16]Lunardi, A., ‘On the linear heat equation with fading memory’, SIAM J. Math. Anal. 21 (5) (1990), 12131224.
[17]Nicola, S. and Pierri, M, ‘A note on -asymptotically periodic functions’, Nonlinear Anal. Real World Appl. 10 (5) (2009), 29372938.
[18]Nunziato, J. W., ‘On heat conduction in materials with memory’, Quart. Appl. Math. 29 (1971), 187204.
[19]Pierri, M., ‘On -asymptotically -periodic functions and applications’, Nonlinear Anal. 75 (2012), 651661.
[20]Utz, W. R. and Waltman, P., ‘Asymptotic almost periodicity of solutions of a system of differential equations’, Proc. Amer. Math. Soc. 18 (1967), 597601.
[21]Sforza, D., ‘Existence in the large for a semilinear integrodifferential equation with infinite delay’, J. Differential Equations 120 (2) (1995), 289303.
[22]Wong, J. S. W. and Burton, T. A., ‘Some properties of solutions of . II’, Monatsh. Math. 69 (1965), 368374.
[23]Zaidman, S., Almost-Periodic Functions in Abstract Spaces, Research Notes in Mathematics, 126 (Pitman, Boston, 1985).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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