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

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Abstract

Consider the homogeneous equation

$$u'(t) = l(u)(t){\rm{ for a}}{\rm{.e}}{\rm{. }}t \in [a,b]$$

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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, The Ariel University Center of Samaria, 44837, Ariel, Israel

    Alexander Domoshnitsky

  2. Institute of Mathematics, Academy of Sciences of the Czech Republic, branch in Brno, Žižkova 22, 616 62, Brno, Czech Republic

    Robert Hakl & Bedřich Půža

Authors
  1. Alexander Domoshnitsky
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  2. Robert Hakl
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  3. Bedřich Půža
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Corresponding author

Correspondence to Alexander Domoshnitsky.

Additional information

For the second and third authors, the research was supported by RVO: 67985840.

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Domoshnitsky, A., Hakl, R. & Půža, B. On the dimension of the solution set to the homogeneous linear functional differential equation of the first order. Czech Math J 62, 1033–1053 (2012). https://doi.org/10.1007/s10587-012-0062-1

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  • DOI: https://doi.org/10.1007/s10587-012-0062-1

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