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Fredholm’s boundary-value problems for differential systems with a single delay. (English) Zbl 1190.34073
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:
34K10Boundary value problems for functional-differential equations
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References:
[1] Azbelev, N. V.; Maksimov, V. P.: Equations with delayed arguments. (English. Russian original), Differ. equ. 18, 1419-1441 (1983) · Zbl 0513.34003
[2] Boichuk, A. A.; Grammatikopoulos, M. K.: Perturbed Fredholm boundary value problems for delay differential systems, Abstr. appl. Anal., No. 15, 843-864 (2003) · Zbl 1077.34069 · doi:10.1155/S1085337503304026
[3] Boichuk, A. A.; Samoilenko, A. M.: Generalized inverse operators and Fredholm boundary value problems, (2004) · Zbl 1083.47003
[4] Hale, J.: Theory of functional differential equations, Applied mathematical sciences 3, 365 (1977) · Zbl 0352.34001
[5] Mallet-Paret, J.: The Fredholm alternative for functional--differential equations of mixed type, J. dynam. Differential equations 11, No. 1, 1-47 (1999) · Zbl 0927.34049 · doi:10.1023/A:1021889401235
[6] Khusainov, D. Ya.; Shuklin, G. V.: Relative controllability in systems with pure delay. (English. Russian original), Internat. appl. Mech. 41, No. 2, 210-221 (2005) · Zbl 1100.34062 · doi:10.1007/s10778-005-0079-3
[7] F.R. Gantmacher, The Theory of Matrices. Vol. 1. Transl. from the Russian by K.A. Hirsch. Reprint of the 1959 translation. (English), Providence, RI, AMS Chelsea Publishing, 374 p. (1998), Vol. 2. Transl. from the Russian by K.A. Hirsch. Reprint of the 1959 translation. (English) Providence, RI, AMS Chelsea Publishing, 276 p. (1998) · Zbl 0927.15002
[8] El’sgol’ts, L. E.; Norkin, S. B.: Introduction to the theory of differential equations with deviating argument (Vvedenie v teoriyu differentsial’nykh uravnenij s otklonyayushchimsya argumentom), (1971) · Zbl 0224.34053
[9] Diblík, J.; Khusainov, D. Ya.; Lukáčová, J.; Ružičková, M.: Representation of a solution of the Cauchy problem for an oscillating system with pure delay. (English. Russian original), Nonlinear oscil. (NY) 11, No. 2, 276-285 (2008) · Zbl 1276.34055
[10] Berezansky, L.; Braverman, E.: Global linearized stability theory for delay differential equations, Nonlinear anal. 71, No. 7, 8, 2614-2624 (2009) · Zbl 1208.34115 · doi:10.1016/j.na.2009.01.147
[11] Diblík, J.; Khusainov, Denys Ya.; Ružičková, M.: Controllability of linear discrete systems with constant coefficients and pure delay, SIAM J. Control optim. 47, No. 3, 1140-1149 (2008) · Zbl 1161.93004 · doi:10.1137/070689085
[12] Ya. Goltser, A. Domoshnitsky, Singular perturbed integro--differential Volterra equation and Drazins inverse singular matrices. Nonlinear Anal., in press (doi:10.1016/j.na.2009.02.048). Corrected proof, Available online 13 February 2009 · Zbl 1238.45006
[13] Hanuštiaková, L.; Olach, R.: Nonoscillatory bounded solutions of neutral differential systems, Nonlinear anal. 68, No. 7, 1816-1824 (2008) · Zbl 1147.34350 · doi:10.1016/j.na.2007.01.014
[14] Krejn, S. G.: Linear equations in Banach space (Linejnye uravneniya v banakhovom prostranstve), (1971) · Zbl 0233.47001