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

@inproceedings{Domoshnitsky2016OnTD,
  title={On the dimension of the solution set to the homogeneous linear functional differential equation of the first order},
  author={Alexander Domoshnitsky and Robert Hakl and Bedřich Pů{\vz}a},
  year={2016}
}
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.