Abstract and Applied Analysis

On periodic solutions of abstract differential equations

Y. S. Eidelman and I. V. Tikhonov

Full-text: Open access

Abstract

Let A be a closed linear operator on a Banach space E. We study periodic solutions of the differential equation dNu(t)/dtN=Au(t) with an arbitrary integer N1.

Article information

Source
Abstr. Appl. Anal., Volume 6, Number 8 (2001), 489-499.

Dates
First available in Project Euclid: 13 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1050266979

Digital Object Identifier
doi:10.1155/S1085337501000537

Mathematical Reviews number (MathSciNet)
MR1880990

Zentralblatt MATH identifier
1010.34053

Subjects
Primary: 34G10: Linear equations [See also 47D06, 47D09]

Citation

Eidelman, Y. S.; Tikhonov, I. V. On periodic solutions of abstract differential equations. Abstr. Appl. Anal. 6 (2001), no. 8, 489--499. doi:10.1155/S1085337501000537. https://projecteuclid.org/euclid.aaa/1050266979


Export citation

References

  • W. Arendt, A. Grabosch, G. Greiner, U. Groh, H. P. Lotz, U. Moustakas, R. Nagel, F. Neubrander, and U. Schlotterbeck, One-Parameter Semigroups of Positive Operators, Lecture Notes in Math., vol. 1184, Springer-Verlag, Berlin, 1986.
  • J. L. Daleckiĭ and M. G. Kreĭn, Stability of Solutions of Differential Equations in Banach Space, Translations of Mathematical Monographs, vol. 43, American Mathematical Society, Rhode Island, 1974.
  • A. A. Dezin, Operators with first derivative with respect to “time” and non-local boundary conditions, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 61–86.
  • Ju. A. Dubinskii, On some differential-operator equations of an arbitrary order, Mat. Sbornik. 90 (1973), 3–22 (Russian).
  • A. Haraux, Nonlinear Evolution Equations–-Global Behavior of Solutions, Lecture Notes in Math., vol. 841, Springer-Verlag, Berlin, 1981.
  • V. K. Ivanov, I. V. Melnikova, and A. I. Filinkov, Differential-Operator Equations and Ill-Posed Problems, Nauka, Moscow, 1994.
  • Ju. I. Ljubič, The classical and local Laplace transform in the abstract Cauchy problem, Uspehi Mat. Nauk 21 (1966), no. 3 (129), 3–51.
  • J. Prüss, On the spectrum of ${C}\sb{0}$-semigroups, Trans. Amer. Math. Soc. 284 (1984), no. 2, 847–857.
  • B. I. Ptashnik, Nekorrektnye granichnye zadachi dlya differentsialnykh uravnenii s chastnymi proizvodnymi [Ill-Posed Boundary Value Problems for Partial Differential Equations], Naukova Dumka, Kiev, 1984 (Russian).
  • L. Schwartz, Analyse Mathématique. II, Hermann, Paris, 1967.
  • O. Vejvoda, L. Herrmann, V. Lovicar, M. Sova, I. Straskraba, and M. Stedry, Partial Differential Equations: Time-Periodic Solutions, Martinus Nijhoff, London, 1982.
  • A. Zygmund, Trigonometric Series, 2nd ed., vol. 1, 2, Cambridge University Press, New York, 1959.