African Diaspora Journal of Mathematics

S-Asymptotically $\omega$-Periodic Functions and Applications to Evolution Equations

J. Blot, P. Cieutat, and G. M. N'Guérékata

Full-text: Open access

Abstract

In this paper, we first study further properties of S-asymptotically $\omega$-periodic functions taking values in Banach spaces including a theorem of composition. Then we apply the results obtained to study the existence and uniqueness of S-asymptotically $\omega$-periodic mild solutions to a nonautonomous semilinear differential equation.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 12, Number 2 (2011), 113-121.

Dates
First available in Project Euclid: 13 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1318535332

Mathematical Reviews number (MathSciNet)
MR2847308

Zentralblatt MATH identifier
1248.34093

Subjects
Primary: 26A33: Fractional derivatives and integrals
Secondary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 34K05: General theory 49J20: Optimal control problems involving partial differential equations 49K20: Problems involving partial differential equations

Keywords
S-asymptotically $\omega$-periodic functions periodic evolutionary process

Citation

Blot, J.; Cieutat, P.; N'Guérékata, G. M. S-Asymptotically $\omega$-Periodic Functions and Applications to Evolution Equations. Afr. Diaspora J. Math. (N.S.) 12 (2011), no. 2, 113--121. https://projecteuclid.org/euclid.adjm/1318535332


Export citation

References

  • H. Gao, K. Wang, F. Wei, X. Ding, Massera-type theorem and asymptotically periodic logistic equations, Nonlinear Analysis, R.W.A., 7 (2006), 1268-1283.
  • R. C. Grimmer, Asymptotically almost periodic solutions of differential equations, SIAM J. Appl. Math. 17 (1969), 109-115.
  • H. R. Henríquez, M. Pierri, P. Táboas, On S-asymptotically $\omega$-periodic functions on Banach spaces and applications, J. Math. Anal. Appl. 343 (2008), 1119-1130.
  • H. R. Henríquez, M. Pierri, P. Táboas, Existence of S-asymptotically $\omega$-periodic solutions for abstract neutral equations, Bull. Austr. Math. Soc. 78 (2008), 365-382.
  • Z. C. Liang, Asymptotically periodic solutions of a class of second order nonlinear differential equations, Proc. Amer. Math. Soc., 99 (4), (1987), 693-699.
  • C. Lizama, G. M. N'Guérékata, Bounded mild solutions for semilinear integro differential equations in Banach spaces, Integral Equations and Operator Theory, 68 (2010), 207-227.
  • G. M. N'Guérékata, Almost Automorphic and Almost Periodic Functions in Abstract Spaces, Kluwer Academic, New York, London, Moscow, 2001.
  • S. Nicola, M. Pierri, A note on S-asymptotically periodic functions, Nonlinear Analysis, R.W.A., 10 (2009), 2937-2938.
  • W. R. Utz, P. Waltman, Asymptotic almost periodicity of solutions of a system of differential equations, Proc. Amer. Math. Soc., 18 (1967), 597-601.
  • J. S. Wong, T. A. Burton, Some properties of solutions of $u"(t)+a(t)f(u)g(u')=0$, II, Monatsh. Math. 69 (1965), 368-374.