On the dimension of the solution set to the homogeneous linear functional differential equation of the first order

Alexander Domoshnitsky; Robert Hakl; Bedřich Půža

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 4, page 1033-1053
  • ISSN: 0011-4642

Abstract

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Consider the homogeneous equation u ' ( t ) = ℓ ( u ) ( t ) for a.e. t ∈ [ a , b ] where ℓ : C ( [ a , b ] ; ℝ ) → L ( [ a , b ] ; ℝ ) is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.

How to cite

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Domoshnitsky, Alexander, Hakl, Robert, and Půža, Bedřich. "On the dimension of the solution set to the homogeneous linear functional differential equation of the first order." Czechoslovak Mathematical Journal 62.4 (2012): 1033-1053. <http://eudml.org/doc/246454>.

@article{Domoshnitsky2012,
abstract = {Consider the homogeneous equation \[ u^\{\prime \}(t)=\ell (u)(t)\qquad \mbox\{for a.e. \} t\in [a,b] \] where $\ell \colon C([a,b];\mathbb \{R\})\rightarrow L([a,b];\mathbb \{R\})$ is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.},
author = {Domoshnitsky, Alexander, Hakl, Robert, Půža, Bedřich},
journal = {Czechoslovak Mathematical Journal},
keywords = {functional differential equation; boundary value problem; differential inequality; solution set; functional differential equation; boundary value problem; differential inequality; solution set},
language = {eng},
number = {4},
pages = {1033-1053},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the dimension of the solution set to the homogeneous linear functional differential equation of the first order},
url = {http://eudml.org/doc/246454},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Domoshnitsky, Alexander
AU - Hakl, Robert
AU - Půža, Bedřich
TI - On the dimension of the solution set to the homogeneous linear functional differential equation of the first order
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 4
SP - 1033
EP - 1053
AB - Consider the homogeneous equation \[ u^{\prime }(t)=\ell (u)(t)\qquad \mbox{for a.e. } t\in [a,b] \] where $\ell \colon C([a,b];\mathbb {R})\rightarrow L([a,b];\mathbb {R})$ is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.
LA - eng
KW - functional differential equation; boundary value problem; differential inequality; solution set; functional differential equation; boundary value problem; differential inequality; solution set
UR - http://eudml.org/doc/246454
ER -

References

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