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

Published online by Cambridge University Press:  30 January 2013

MICHELLE PIERRI  and
VANESSA ROLNIK
MICHELLE PIERRI*
Affiliation:
Departamento de Computação e Matemática da Faculdade de Filosofia Ciências e Letras, de Ribeirão Preto. Universidade de São Paulo, Ribeirão Preto, SP, Brazil
VANESSA ROLNIK
Affiliation:
Departamento de Computação e Matemática da Faculdade de Filosofia Ciências e Letras, de Ribeirão Preto. Universidade de São Paulo, Ribeirão Preto, SP, Brazil email [email protected]
*
✉[email protected]
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Abstract

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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.

Keywords

pseudo 𝓢-asymptotically periodic functions𝓢-asymptotically periodic functionasymptotically periodic functionneutral equationmild solution
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 2 , April 2013 , pp. 238 - 254
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc.

References

de Andrade, B. and Cuevas, C., ‘$ \mathcal{S} $-asymptotically $\omega $-periodic and asymptotically $\omega $-periodic solutions to semilinear Cauchy problems with non dense domain’, Nonlinear Anal. 72 (2010), 3190–3208.CrossRefGoogle Scholar
Corduneanu, C., Almost Periodic Functions, 2nd edn (Chelsea, New York, 1989).Google Scholar
Cuevas, C. and Lizama, C., ‘$ \mathcal{S} $-asymptotically $\omega $-periodic solutions for semilinear Volterra equations’, Math. Methods Appl. Sci. 33 (13) (2010), 1628–1636.CrossRefGoogle Scholar
Cuevas, C. and de Souza, J. C., ‘$ \mathcal{S} $-asymptotically $\omega $-periodic solutions of semilinear fractional integro-differential equations’, Appl. Math. Lett. 22 (6) (2009), 865–870.CrossRefGoogle Scholar
Cuevas, C. and de Souza, J. C., ‘Existence of $ \mathcal{S} $-asymptotically $\omega $-periodic solutions for fractional order functional integro-differential equations with infinite delay’, Nonlinear Anal. 72 (3–4) (2010), 1683–1689.CrossRefGoogle Scholar
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).Google Scholar
Gurtin, M. E. and Pipkin, A. C., ‘A general theory of heat conduction with finite wave speed’, Arch. Rat. Mech. Anal. 31 (1968), 113–126.CrossRefGoogle Scholar
Henríquez, H., Pierri, M. and Táboas, P., ‘Existence of $ \mathcal{S} $-asymptotically $\omega $-periodic solutions for abstract neutral equations’, Bull. Aust. Math. Soc. 78 (3) (2008), 365–382.CrossRefGoogle Scholar
Henríquez, H., Pierri, M. and Táboas, P., ‘On $ \mathcal{S} $-asymptotically $\omega $-periodic functions on Banach spaces and applications’, J. Math. Anal. Appl. 343 (2) (2008), 1119–1130.CrossRefGoogle Scholar
Hernández, E., ‘Existence results for partial neutral integro-differential equations with unbounded delay’, J. Math. Anal. Appl. 292 (1) (2004), 194–210.CrossRefGoogle Scholar
Hernández, E. and Henríquez, H., ‘Existence results for partial neutral functional differential equation with unbounded delay’, J. Math. Anal. Appl. 221 (2) (1998), 452–475.CrossRefGoogle Scholar
Hernández, E. and O’Regan., D., ‘${C}^{\alpha } $-Hölder classical solutions for non-autonomous neutral differential equations’, Discrete Contin. Dyn. Syst. A 29 (1) (2011), 241–260.CrossRefGoogle Scholar
Hernández, E. and O’Regan, D., ‘On a new class of abstract neutral differential equations’, J. Funct. Anal. 261 (12) (2011), 3457–3481.CrossRefGoogle Scholar
Levitan, B. M. and Zhikov, V. V., Almost Periodic Functions and Differential Equations (Cambridge University Press, Cambridge, 1982).Google Scholar
Liang, Z. C., ‘Asymptotically periodic solutions of a class of second order nonlinear differential equations’, Proc. Amer. Math. Soc. 99 (4) (1987), 693–699.CrossRefGoogle Scholar
Lunardi, A., ‘On the linear heat equation with fading memory’, SIAM J. Math. Anal. 21 (5) (1990), 1213–1224.CrossRefGoogle Scholar
Nicola, S. and Pierri, M, ‘A note on $ \mathcal{S} $-asymptotically periodic functions’, Nonlinear Anal. Real World Appl. 10 (5) (2009), 2937–2938.CrossRefGoogle Scholar
Nunziato, J. W., ‘On heat conduction in materials with memory’, Quart. Appl. Math. 29 (1971), 187–204.CrossRefGoogle Scholar
Pierri, M., ‘On $S$-asymptotically $\omega $-periodic functions and applications’, Nonlinear Anal. 75 (2012), 651–661.CrossRefGoogle Scholar
Utz, W. R. and Waltman, P., ‘Asymptotic almost periodicity of solutions of a system of differential equations’, Proc. Amer. Math. Soc. 18 (1967), 597–601.CrossRefGoogle Scholar
Sforza, D., ‘Existence in the large for a semilinear integrodifferential equation with infinite delay’, J. Differential Equations 120 (2) (1995), 289–303.CrossRefGoogle Scholar
Wong, J. S. W. and Burton, T. A., ‘Some properties of solutions of ${u}^{\prime \prime } (t)+ a(t)f(u)g({u}^{\prime } )= 0$. II’, Monatsh. Math. 69 (1965), 368–374.CrossRefGoogle Scholar
Zaidman, S., Almost-Periodic Functions in Abstract Spaces, Research Notes in Mathematics, 126 (Pitman, Boston, 1985).Google Scholar