Geodesic
On a two point linear boundary value problem for system of ODEs with deviating arguments
Archivum mathematicum, Tome 38 (2002) no. 2, pp. 101-118 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Two point boundary value problem for the linear system of ordinary differential equations with deviating arguments \[{{x}^{\prime }(t) ={A}(t){x}(\tau _{11}(t))+{B}(t){u}(\tau _{12}(t)) +{q}_1(t)\,, {u}^{\prime }(t) ={C}(t){x}(\tau _{21}(t))+{D}(t){u}(\tau _{22}(t)) +{q}_2(t)\,, \alpha _{11} {x}(0) + \alpha _{12} {u}(0) = {c}_0, \quad \alpha _{21} {x}(T) + \alpha _{22} {u}(T) = {c}_T} \] is considered. For this problem the sufficient condition for existence and uniqueness of solution is obtained. The same approach as in [2], [3] is applied.
Two point boundary value problem for the linear system of ordinary differential equations with deviating arguments \[{{x}^{\prime }(t) ={A}(t){x}(\tau _{11}(t))+{B}(t){u}(\tau _{12}(t)) +{q}_1(t)\,, {u}^{\prime }(t) ={C}(t){x}(\tau _{21}(t))+{D}(t){u}(\tau _{22}(t)) +{q}_2(t)\,, \alpha _{11} {x}(0) + \alpha _{12} {u}(0) = {c}_0, \quad \alpha _{21} {x}(T) + \alpha _{22} {u}(T) = {c}_T} \] is considered. For this problem the sufficient condition for existence and uniqueness of solution is obtained. The same approach as in [2], [3] is applied.
Classification : 34B05, 34B10
Keywords: existence and uniqueness of solution; two point linear boundary value problem; linear system of ordinary differential equations; deviating argument; delay 
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Kubalčík, Jan. On a two point linear boundary value problem for system of ODEs with deviating arguments. Archivum mathematicum, Tome 38 (2002) no. 2, pp. 101-118. http://geodesic.mathdoc.fr/item/ARM_2002_38_2_a2/

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