Almost-periodic solutions in various metrics of higher-order differential equations with a nonlinear restoring term

Ján Andres; Alberto Maria Bersani; Lenka Radová

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2006)

  • Volume: 45, Issue: 1, page 7-29
  • ISSN: 0231-9721

Abstract

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Almost-periodic solutions in various metrics (Stepanov, Weyl, Besicovitch) of higher-order differential equations with a nonlinear Lipschitz-continuous restoring term are investigated. The main emphasis is focused on a Lipschitz constant which is the same as for uniformly almost-periodic solutions treated in [A1] and much better than those from our investigations for differential systems in [A2], [A3], [AB], [ABL], [AK]. The upper estimates of ε for ε -almost-periods of solutions and their derivatives are also deduced under various restrictions imposed on the constant coefficients of the linear differential operator on the left-hand side of the given equation. Besides the existence, uniqueness and localization of almost-periodic solutions and their derivatives are established.

How to cite

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Andres, Ján, Bersani, Alberto Maria, and Radová, Lenka. "Almost-periodic solutions in various metrics of higher-order differential equations with a nonlinear restoring term." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 45.1 (2006): 7-29. <http://eudml.org/doc/32508>.

@article{Andres2006,
abstract = {Almost-periodic solutions in various metrics (Stepanov, Weyl, Besicovitch) of higher-order differential equations with a nonlinear Lipschitz-continuous restoring term are investigated. The main emphasis is focused on a Lipschitz constant which is the same as for uniformly almost-periodic solutions treated in [A1] and much better than those from our investigations for differential systems in [A2], [A3], [AB], [ABL], [AK]. The upper estimates of $\varepsilon $ for $\varepsilon $-almost-periods of solutions and their derivatives are also deduced under various restrictions imposed on the constant coefficients of the linear differential operator on the left-hand side of the given equation. Besides the existence, uniqueness and localization of almost-periodic solutions and their derivatives are established.},
author = {Andres, Ján, Bersani, Alberto Maria, Radová, Lenka},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Almost-periodic solutions; various metrics; higher-order differential equation; nonlinear restoring term; existence and uniqueness criteria; Almost periodic solution; existence and uniqueness},
language = {eng},
number = {1},
pages = {7-29},
publisher = {Palacký University Olomouc},
title = {Almost-periodic solutions in various metrics of higher-order differential equations with a nonlinear restoring term},
url = {http://eudml.org/doc/32508},
volume = {45},
year = {2006},
}

TY - JOUR
AU - Andres, Ján
AU - Bersani, Alberto Maria
AU - Radová, Lenka
TI - Almost-periodic solutions in various metrics of higher-order differential equations with a nonlinear restoring term
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2006
PB - Palacký University Olomouc
VL - 45
IS - 1
SP - 7
EP - 29
AB - Almost-periodic solutions in various metrics (Stepanov, Weyl, Besicovitch) of higher-order differential equations with a nonlinear Lipschitz-continuous restoring term are investigated. The main emphasis is focused on a Lipschitz constant which is the same as for uniformly almost-periodic solutions treated in [A1] and much better than those from our investigations for differential systems in [A2], [A3], [AB], [ABL], [AK]. The upper estimates of $\varepsilon $ for $\varepsilon $-almost-periods of solutions and their derivatives are also deduced under various restrictions imposed on the constant coefficients of the linear differential operator on the left-hand side of the given equation. Besides the existence, uniqueness and localization of almost-periodic solutions and their derivatives are established.
LA - eng
KW - Almost-periodic solutions; various metrics; higher-order differential equation; nonlinear restoring term; existence and uniqueness criteria; Almost periodic solution; existence and uniqueness
UR - http://eudml.org/doc/32508
ER -

References

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