Geodesic
On an antiperiodic type boundary value problem for first order linear functional differential equations
Archivum mathematicum, Tome 38 (2002) no. 2, pp. 149-160 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Nonimprovable, in a certain sense, sufficient conditions for the unique solvability of the boundary value problem \[ u^{\prime }(t)=\ell (u)(t)+q(t),\qquad u(a)+\lambda u(b)=c \] are established, where $\ell :C([a,b];R)\rightarrow L([a,b];R)$ is a linear bounded operator, $q\in L([a,b];R)$, $\lambda \in R_+$, and $c\in R$. The question on the dimension of the solution space of the homogeneous problem \[ u^{\prime }(t)=\ell (u)(t),\qquad u(a)+\lambda u(b)=0 \] is discussed as well.
Nonimprovable, in a certain sense, sufficient conditions for the unique solvability of the boundary value problem \[ u^{\prime }(t)=\ell (u)(t)+q(t),\qquad u(a)+\lambda u(b)=c \] are established, where $\ell :C([a,b];R)\rightarrow L([a,b];R)$ is a linear bounded operator, $q\in L([a,b];R)$, $\lambda \in R_+$, and $c\in R$. The question on the dimension of the solution space of the homogeneous problem \[ u^{\prime }(t)=\ell (u)(t),\qquad u(a)+\lambda u(b)=0 \] is discussed as well.
Classification : 34K13
Keywords: linear functional differential equation; antiperiodic type BVP; solvability and unique solvability 
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     author = {Hakl, R. and Lomtatidze, A. and \v{S}remr, J.},
     title = {On an antiperiodic type boundary value problem for first order linear functional differential equations},
     journal = {Archivum mathematicum},
     pages = {149--160},
     year = {2002},
     volume = {38},
     number = {2},
     mrnumber = {1909595},
     zbl = {1087.34042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2002_38_2_a5/}
}
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Hakl, R.; Lomtatidze, A.; Šremr, J. On an antiperiodic type boundary value problem for first order linear functional differential equations. Archivum mathematicum, Tome 38 (2002) no. 2, pp. 149-160. http://geodesic.mathdoc.fr/item/ARM_2002_38_2_a5/