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 -