# On Cauchy problem for first order nonlinear functional differential equations of non-Volterra’s type

• Volume: 52, Issue: 4, page 673-690
• ISSN: 0011-4642

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## Abstract

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On the segment $I=\left[a,b\right]$ consider the problem ${u}^{\text{'}}\left(t\right)=f\left(u\right)\left(t\right),\phantom{\rule{1.0em}{0ex}}u\left(a\right)=c,$ where $f\phantom{\rule{0.222222em}{0ex}}C\left(I,ℝ\right)\to L\left(I,ℝ\right)$ is a continuous, in general nonlinear operator satisfying Carathéodory condition, and $c\in ℝ$. The effective sufficient conditions guaranteeing the solvability and unique solvability of the considered problem are established. Examples verifying the optimality of obtained results are given, as well.

## How to cite

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Bravyi, E., Hakl, Robert, and Lomtatidze, Alexander. "On Cauchy problem for first order nonlinear functional differential equations of non-Volterra’s type." Czechoslovak Mathematical Journal 52.4 (2002): 673-690. <http://eudml.org/doc/30734>.

@article{Bravyi2002,
abstract = {On the segment $I=[a,b]$ consider the problem $u^\{\prime \}(t)=f(u)(t) , \quad u(a)=c,$ where $f\:C(I,\mathbb \{R\})\rightarrow L(I,\mathbb \{R\})$ is a continuous, in general nonlinear operator satisfying Carathéodory condition, and $c\in \mathbb \{R\}$. The effective sufficient conditions guaranteeing the solvability and unique solvability of the considered problem are established. Examples verifying the optimality of obtained results are given, as well.},
author = {Bravyi, E., Hakl, Robert, Lomtatidze, Alexander},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlinear functional differential equation; initial value problem; non–Volterra’s type operator; nonlinear functional-differential equation; initial value problem; non-Volterra-type operator},
language = {eng},
number = {4},
pages = {673-690},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On Cauchy problem for first order nonlinear functional differential equations of non-Volterra’s type},
url = {http://eudml.org/doc/30734},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Bravyi, E.
AU - Hakl, Robert
AU - Lomtatidze, Alexander
TI - On Cauchy problem for first order nonlinear functional differential equations of non-Volterra’s type
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 4
SP - 673
EP - 690
AB - On the segment $I=[a,b]$ consider the problem $u^{\prime }(t)=f(u)(t) , \quad u(a)=c,$ where $f\:C(I,\mathbb {R})\rightarrow L(I,\mathbb {R})$ is a continuous, in general nonlinear operator satisfying Carathéodory condition, and $c\in \mathbb {R}$. The effective sufficient conditions guaranteeing the solvability and unique solvability of the considered problem are established. Examples verifying the optimality of obtained results are given, as well.
LA - eng
KW - nonlinear functional differential equation; initial value problem; non–Volterra’s type operator; nonlinear functional-differential equation; initial value problem; non-Volterra-type operator
UR - http://eudml.org/doc/30734
ER -

## References

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