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

Alexander Domoshnitsky; Robert Hakl; Bedřich Půža

doi:10.1007/s10587-012-0062-1

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

Alexander Domoshnitsky
, Robert Hakl
, Bedřich Půža

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Consider the homogeneous equation, 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.

Original language	English
Pages (from-to)	1033-1053
Number of pages	21
Journal	Czechoslovak Mathematical Journal
Volume	62
Issue number	4
DOIs	https://doi.org/10.1007/s10587-012-0062-1
State	Published - Dec 2012

Keywords

boundary value problem
differential inequality
functional differential equation
solution set

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10.1007/s10587-012-0062-1

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abstract = "Consider the homogeneous equation, 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.",

keywords = "boundary value problem, differential inequality, functional differential equation, solution set",

author = "Alexander Domoshnitsky and Robert Hakl and Bed{\v r}ich Pů{\v z}a",

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AU - Domoshnitsky, Alexander

AU - Hakl, Robert

AU - Půža, Bedřich

N1 - Funding Information: For the second and third authors, the research was supported by RVO: 67985840.

PY - 2012/12

Y1 - 2012/12

N2 - Consider the homogeneous equation, 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.

AB - Consider the homogeneous equation, 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.

KW - boundary value problem

KW - differential inequality

KW - functional differential equation

KW - solution set

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ER -

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

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