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

E. Bravyi; Robert Hakl; Alexander Lomtatidze

Czechoslovak Mathematical Journal (2002)

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

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topBravyi, 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 -

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## Citations in EuDML Documents

top- Robert Hakl, Alexander Lomtatidze, Jiří Šremr, Solvability of a periodic type boundary value problem for first order scalar functional differential equations
- Robert Hakl, Alexander Lomtatidze, Jiří Šremr, On an antiperiodic type boundary value problem for first order linear functional differential equations

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