Almost periodic solutions with a prescribed spectrum of systems of linear and quasilinear differential equations with almost periodic coefficients and constant time lag (Cauchy integral)

Alexandr Fischer

Mathematica Bohemica (1999)

  • Volume: 124, Issue: 4, page 351-379
  • ISSN: 0862-7959

Abstract

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This paper generalizes earlier author's results where the linear and quasilinear equations with constant coefficients were treated. Here the method of limit passages and a fixed-point theorem is used for the linear and quasilinear equations with almost periodic coefficients.

How to cite

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Fischer, Alexandr. "Almost periodic solutions with a prescribed spectrum of systems of linear and quasilinear differential equations with almost periodic coefficients and constant time lag (Cauchy integral)." Mathematica Bohemica 124.4 (1999): 351-379. <http://eudml.org/doc/248462>.

@article{Fischer1999,
abstract = {This paper generalizes earlier author's results where the linear and quasilinear equations with constant coefficients were treated. Here the method of limit passages and a fixed-point theorem is used for the linear and quasilinear equations with almost periodic coefficients.},
author = {Fischer, Alexandr},
journal = {Mathematica Bohemica},
keywords = {almost periodic function; Fourier coefficient; Fourier exponent; spectrum of almost periodic function; almost periodic system of differential equations; formal almost periodic solution; distance of two spectra; time lag; almost periodic function; Fourier coefficient; Fourier exponent; spectrum of almost periodic function; almost periodic system of differential equations; formal almost periodic solution; distance of two spectra; time lag},
language = {eng},
number = {4},
pages = {351-379},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Almost periodic solutions with a prescribed spectrum of systems of linear and quasilinear differential equations with almost periodic coefficients and constant time lag (Cauchy integral)},
url = {http://eudml.org/doc/248462},
volume = {124},
year = {1999},
}

TY - JOUR
AU - Fischer, Alexandr
TI - Almost periodic solutions with a prescribed spectrum of systems of linear and quasilinear differential equations with almost periodic coefficients and constant time lag (Cauchy integral)
JO - Mathematica Bohemica
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 124
IS - 4
SP - 351
EP - 379
AB - This paper generalizes earlier author's results where the linear and quasilinear equations with constant coefficients were treated. Here the method of limit passages and a fixed-point theorem is used for the linear and quasilinear equations with almost periodic coefficients.
LA - eng
KW - almost periodic function; Fourier coefficient; Fourier exponent; spectrum of almost periodic function; almost periodic system of differential equations; formal almost periodic solution; distance of two spectra; time lag; almost periodic function; Fourier coefficient; Fourier exponent; spectrum of almost periodic function; almost periodic system of differential equations; formal almost periodic solution; distance of two spectra; time lag
UR - http://eudml.org/doc/248462
ER -

References

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  1. Amerio L., Prouse G., Almost Periodic Functious and Functional Equations, N.Y. Van Nostrand Reinhold Company, 1971. (1971) MR0275061
  2. Bohr H., Zur Theorie der fastperiodischen Funktionen, Acta Math. 45 (1925), 29-127; 46 (1925), 101-214; 47 (1926), 237-281. (1925) MR1555216
  3. Bochner S., 10.1007/BF01209156, Math. Ann. 96 (1927), 119-147. (1927) MR1512308DOI10.1007/BF01209156
  4. Bochner S., 10.1007/BF02547790, Acta Math. 61 (1933), 149-184. (1933) Zbl0007.11201MR1555374DOI10.1007/BF02547790
  5. Fink A. M., Almost Periodic Differential Equations, Lecture Notes in Mathematics, Springer, New York, 1978. (1978) MR0460799
  6. Fischer A., Existence of almost periodic solution of systems of linear and quasilinear differential equations with time lag, Czechoslovak Math J. 106 (1981). (1981) MR0629724
  7. Levitan B. M., Almost Periodic Functions, GIZTL, Moskva, 1953. (In Russian.) (1953) Zbl1222.42002MR0060629
  8. Levitan B. M., Žikov V. V., Almost Periodic Functions and Differential Equations, IMU, Moskva, 1978. (In Russian.) (1978) MR0509035
  9. Šimanov S. N, Almost periodic functions and differential equations with tíme lag, VUZ SSSR, Matematika 4(5) (1959). (In Russian.) (1959) 

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