Geodesic
On the dimension of the solution set to the homogeneous linear functional differential equation of the first order
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 1033-1053
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Consider the homogeneous equation $$ u'(t)=\ell (u)(t)\qquad \mbox {for a.e. } t\in [a,b] $$ where $\ell \colon C([a,b];\Bbb R)\to L([a,b];\Bbb R)$ 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.
Consider the homogeneous equation $$ u'(t)=\ell (u)(t)\qquad \mbox {for a.e. } t\in [a,b] $$ where $\ell \colon C([a,b];\Bbb R)\to L([a,b];\Bbb R)$ 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.
DOI : 10.1007/s10587-012-0062-1
Classification : 34K06, 34K10
Keywords: functional differential equation; boundary value problem; differential inequality; solution set 
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Domoshnitsky, Alexander; Hakl, Robert; Půža, Bedřich. On the dimension of the solution set to the homogeneous linear functional differential equation of the first order. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 1033-1053. doi: 10.1007/s10587-012-0062-1

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