Fredholm’s boundary-value problems for differential systems with a single delay |
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Authors: | A Boichuk D Khusainov |
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Institution: | a ?ilina University, ?ilina, Slovak Republic b Kiev University, Kiev, Ukraine |
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Abstract: | Conditions are derived for the existence of solutions of linear Fredholm’s boundary-value problems for systems of ordinary differential equations with constant coefficients and a single delay. Utilizing a delayed matrix exponential and a method of pseudo-inverse by Moore-Penrose matrices led to an explicit and analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a differential system with a single delay. |
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Keywords: | Fredholm&rsquo s boundary-value problem Differential systems Single delay Delayed matrix exponential Pseudo-inverse matrix |
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