The periodic problem for the second order integro-differential equations with distributed deviation

Sulkhan Mukhigulashvili; Veronika Novotná

Mathematica Bohemica (2021)

  • Volume: 146, Issue: 2, page 167-183
  • ISSN: 0862-7959

Abstract

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We study the question of the unique solvability of the periodic type problem for the second order linear integro-differential equation with distributed argument deviation u ' ' ( t ) = p 0 ( t ) u ( t ) + ∫ 0 ω p ( t , s ) u ( τ ( t , s ) ) d s + q ( t ) , and on the basis of the obtained results by the a priori boundedness principle we prove the new results on the solvability of periodic type problem for the second order nonlinear functional differential equations, which are close to the linear integro-differential equations. The proved results are optimal in some sense.

How to cite

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Mukhigulashvili, Sulkhan, and Novotná, Veronika. "The periodic problem for the second order integro-differential equations with distributed deviation." Mathematica Bohemica 146.2 (2021): 167-183. <http://eudml.org/doc/297964>.

@article{Mukhigulashvili2021,
abstract = {We study the question of the unique solvability of the periodic type problem for the second order linear integro-differential equation with distributed argument deviation \[ u^\{\prime \prime \}(t)=p\_0(t)u(t)+\int \_\{0\}^\{\omega \}p(t,s)u(\tau (t,s)) \{\rm d\}s+ q(t), \] and on the basis of the obtained results by the a priori boundedness principle we prove the new results on the solvability of periodic type problem for the second order nonlinear functional differential equations, which are close to the linear integro-differential equations. The proved results are optimal in some sense.},
author = {Mukhigulashvili, Sulkhan, Novotná, Veronika},
journal = {Mathematica Bohemica},
keywords = {linear integro-differential equation; periodic problem; distributed deviation; solvability},
language = {eng},
number = {2},
pages = {167-183},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The periodic problem for the second order integro-differential equations with distributed deviation},
url = {http://eudml.org/doc/297964},
volume = {146},
year = {2021},
}

TY - JOUR
AU - Mukhigulashvili, Sulkhan
AU - Novotná, Veronika
TI - The periodic problem for the second order integro-differential equations with distributed deviation
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 146
IS - 2
SP - 167
EP - 183
AB - We study the question of the unique solvability of the periodic type problem for the second order linear integro-differential equation with distributed argument deviation \[ u^{\prime \prime }(t)=p_0(t)u(t)+\int _{0}^{\omega }p(t,s)u(\tau (t,s)) {\rm d}s+ q(t), \] and on the basis of the obtained results by the a priori boundedness principle we prove the new results on the solvability of periodic type problem for the second order nonlinear functional differential equations, which are close to the linear integro-differential equations. The proved results are optimal in some sense.
LA - eng
KW - linear integro-differential equation; periodic problem; distributed deviation; solvability
UR - http://eudml.org/doc/297964
ER -

References

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  9. Mukhigulashvili, S., Partsvania, N., Půža, B., 10.1016/j.na.2011.02.002, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74 (2011), 3232-3241. (2011) Zbl1225.34073MR2793558DOI10.1016/j.na.2011.02.002
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