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

0384217 - MÚ 2013 RIV CZ eng J - Journal Article
Domoshnitsky, A. - Hakl, Robert - Půža, Bedřich
On the dimension of the solution set to the homogeneous linear differential equation of the first order.
Czechoslovak Mathematical Journal. Roč. 62, č. 4 (2012), s. 1033-1053. ISSN 0011-4642. E-ISSN 1572-9141
Institutional support: RVO:67985840
Keywords : functional differential equation * boundary value problem * solution set
Subject RIV: BA - General Mathematics
Impact factor: 0.300, year: 2012
http://link.springer.com/article/10.1007/s10587-012-0062-1

Consider the homogeneous equation $$u'(t)=/ell(u)(t)/qquadfor a.e. t/in[a,b]$$ where $/ell C([a,b];/Bbb R)/to L([a,b];/Bbb R)$ 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.
Permanent Link: http://hdl.handle.net/11104/0213932