Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

E. Bravyi; Robert Hakl; Alexander Lomtatidze

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 3, page 513-530
  • ISSN: 0011-4642

Abstract

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Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem u ' ( t ) = ℓ ( u ) ( t ) + q ( t ) , u ( a ) = c , where ℓ C ( I , ℝ ) → L ( I , ℝ ) is a linear bounded operator, q ∈ L ( I , ℝ ) , and c ∈ ℝ , are established.

How to cite

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Bravyi, E., Hakl, Robert, and Lomtatidze, Alexander. "Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations." Czechoslovak Mathematical Journal 52.3 (2002): 513-530. <http://eudml.org/doc/30720>.

@article{Bravyi2002,
abstract = {Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem \[ u^\{\prime \}(t)=\ell (u)(t)+q(t), \qquad u(a)=c, \] where $\ell \:C(I,\mathbb \{R\})\rightarrow L(I,\mathbb \{R\})$ is a linear bounded operator, $q\in L(I,\mathbb \{R\})$, and $c\in \mathbb \{R\}$, are established.},
author = {Bravyi, E., Hakl, Robert, Lomtatidze, Alexander},
journal = {Czechoslovak Mathematical Journal},
keywords = {linear functional differential equations; Cauchy problem; existence and uniqueness; differential inequalities; linear functional-differential equations; Cauchy problem; existence and uniqueness; differential inequalities},
language = {eng},
number = {3},
pages = {513-530},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations},
url = {http://eudml.org/doc/30720},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Bravyi, E.
AU - Hakl, Robert
AU - Lomtatidze, Alexander
TI - Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 3
SP - 513
EP - 530
AB - Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem \[ u^{\prime }(t)=\ell (u)(t)+q(t), \qquad u(a)=c, \] where $\ell \:C(I,\mathbb {R})\rightarrow L(I,\mathbb {R})$ is a linear bounded operator, $q\in L(I,\mathbb {R})$, and $c\in \mathbb {R}$, are established.
LA - eng
KW - linear functional differential equations; Cauchy problem; existence and uniqueness; differential inequalities; linear functional-differential equations; Cauchy problem; existence and uniqueness; differential inequalities
UR - http://eudml.org/doc/30720
ER -

References

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  1. Introduction to the Theory of Functional Differential Equations, Nauka, Moscow, 1991. (Russian) (1991) MR1144998
  2. On multi-point boundary value problems for systems of functional differential and difference equations, Mem. Differential Equations Math. Phys. 5 (1995), 1–113. (1995) MR1415806
  3. Ordinary Differential Equations, John Wiley, New York, 1964. (1964) Zbl0125.32102MR0171038
  4. 10.1023/A:1022829931363, Czechoslovak Math. J. 47 (1997), 341–373. (1997) MR1452425DOI10.1023/A:1022829931363
  5. Differential and integral equations: boundary value problems and adjoints, Academia, Praha, 1979. (1979) MR0542283

Citations in EuDML Documents

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  1. Robert Hakl, Alexander Lomtatidze, A note on the Cauchy problem for first order linear differential equations with a deviating argument
  2. Alexander Domoshnitsky, Robert Hakl, Bedřich Půža, On the dimension of the solution set to the homogeneous linear functional differential equation of the first order
  3. E. Bravyi, Robert Hakl, Alexander Lomtatidze, On Cauchy problem for first order nonlinear functional differential equations of non-Volterra’s type
  4. Robert Hakl, Alexander Lomtatidze, Jiří Šremr, Solvability of a periodic type boundary value problem for first order scalar functional differential equations
  5. Robert Hakl, Alexander Lomtatidze, Jiří Šremr, On an antiperiodic type boundary value problem for first order linear functional differential equations

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