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Zbl 1190.34073
Boichuk, A.; Dibl{\'\i}k, J.; Khusainov, D.; Ruužičková, M.
Fredholm's boundary-value problems for differential systems with a single delay. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 5, A, 2251-2258 (2010). ISSN 0362-546X

Summary: 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.

MSC 2000:: *34K10 Boundary value problems for functional-differential equations

Keywords: Fredholm's boundary-value problem; differential systems; single delay; delayed matrix exponential; pseudo-inverse matrix

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Zentralblatt MATH Berlin [Germany]