TY - JOUR

T1 - On the dimension of the solution set to the homogeneous linear functional differential equation of the first order

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

UR - http://www.scopus.com/inward/record.url?scp=84872311686&partnerID=8YFLogxK

U2 - 10.1007/s10587-012-0062-1

DO - 10.1007/s10587-012-0062-1

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AN - SCOPUS:84872311686

SN - 0011-4642

VL - 62

SP - 1033

EP - 1053

JO - Czechoslovak Mathematical Journal

JF - Czechoslovak Mathematical Journal

IS - 4

ER -