Geodesic
On the solvability of the periodic boundary value problem for a linear functional differential equation
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2009), pp. 12-24 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Necessary and sufficient conditions for the uniquely solvability of the periodic boundary value problem for functional differential equations are obtained.
Keywords: functional differential equations, boundary value problems, periodic problem, Green function. 
@article{VUU_2009_3_a1,
     author = {E. I. Bravyi},
     title = {On the solvability of the periodic boundary value problem for a~linear functional differential equation},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {12--24},
     year = {2009},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2009_3_a1/}
}
TY  - JOUR
AU  - E. I. Bravyi
TI  - On the solvability of the periodic boundary value problem for a linear functional differential equation
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2009
SP  - 12
EP  - 24
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VUU_2009_3_a1/
LA  - ru
ID  - VUU_2009_3_a1
ER  - 
%0 Journal Article
%A E. I. Bravyi
%T On the solvability of the periodic boundary value problem for a linear functional differential equation
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2009
%P 12-24
%N 3
%U http://geodesic.mathdoc.fr/item/VUU_2009_3_a1/
%G ru
%F VUU_2009_3_a1
E. I. Bravyi. On the solvability of the periodic boundary value problem for a linear functional differential equation. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2009), pp. 12-24. http://geodesic.mathdoc.fr/item/VUU_2009_3_a1/

[1] Hakl R., Lomtatidze A., Sremr J., “Solvability and the unique solvability of a periodic type boundary value problem for first order scalar functional differential equations”, Georgian Math. J., 9:3 (2002), 525–547 | MR | Zbl

[2] Hakl R., Lomtatidze A., Sremr J., Some Boundary Value Problems For First Order Scalar Functional Differential Eequations, Folia Facult. Scien. Natur. Masar. Brunensis. Mathematica, Brno, 2002, 299 pp. | Zbl

[3] Lomtatidze A. G., Puzha B., Khakl R., “O periodicheskikh kraevykh zadachakh dlya funktsionalno-differentsialnykh uravnenii pervogo poryadka”, Differents. uravneniya, 39:3 (2003), 320–327 | MR | Zbl

[4] Hakl R., “On periodic-type boundary value problems for functional differential equations with a positively homogeneous operator”, Miskolc Math. Notes, 5:1 (2004), 33–55 | MR | Zbl

[5] Mukhigulashvili S., “On a periodic boundary value problem for second-order linear functional differential equations”, Boundary Value Problems, 2005, no. 3, 247–261 | DOI | MR | Zbl

[6] Kiguradze I., Mukhigulashvili S., “On periodic solutions of two-dimensional nonautonomous differential systems”, Nonlinear Anal. Theory, Methods, Appl., 60:2 (2005), 241–256 | DOI | MR | Zbl

[7] Hakl R., Mukhigulashvili S., “On one estimate for periodic functions”, Georgian Math. J., 12:1 (2005), 97–114 | MR | Zbl

[8] Mukhigulashvili S., Puza B., “On a Periodic Boundary Value Problem for Cyclic Feedback Type Linear Functional Differential Systems”, Mem. Differential Equations Math. Phys., 40 (2007), 67–75 | MR | Zbl

[9] Mukhigulashvili S., Puza B., “On a Periodic Boundary Value Problem for Third Order Linear Functional Differential Equations”, Functional Differential Equations, 14:3–4 (2007), 347–362 | MR

[10] Hakl R., “On a Periodic Type Boundary Value Problem For Functional Differential Equations with A Positively Homogeneous Operator”, Mem. Differential Equations Math. Phys., 40 (2007), 17–54 | MR | Zbl

[11] Mukhigulashvili S., “On a periodic boundary value problem for third order linear functional differential equations”, Nonlinear Anal. Theory, Methods, Appl., 66:2 (2007), 527–535 | DOI | MR | Zbl

[12] Mukhigulashvili S., “On a periodic boundary value problem for cyclic feedback type linear functional differential systems”, Arch. Math., 87:3 (2007), 255–260 | DOI | MR

[13] Bravyi E. I., “Ob odnoznachnoi razreshimosti periodicheskoi kraevoi zadachi dlya lineinogo funktsionalno-differentsialnogo uravneniya”, Teoriya upravleniya i matematicheskoe modelirovanie, materialy nauch. konf.-seminara, IzhGTU, Izhevsk, 2008, 8–11

[14] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Elementy sovremennoi teorii funktsionalno-differentsialnykh uravnenii. Metody i prilozheniya, Institut kompyuternykh issledovanii, M., 2002, 384 pp.

[15] Komlenko Yu. V., Tonkov E. L., “O multiplikatorakh lineinogo periodicheskogo differentsialnogo uravneniya s otklonyayuschimsya argumentom”, Sib. mat. zhurn., 15:4 (1974), 835–844 | MR | Zbl

[16] Lasota A., Opial Z., “Sur les solutions periodiques des equations differentielles ordinaires”, Ann. Pol. Math., 6:1 (1964), 69–94 | MR

[17] Komlenko Yu. V., Tonkov E. L., “Periodicheskaya zadacha dlya obyknovennogo differentsialnogo uravneniya vtorogo poryadka”, DAN, 179:1 (1968), 17–19 | MR | Zbl

[18] Tonkov E. L., Yutkin G. I., “Periodicheskie resheniya i ustoichivost lineinogo differentsialnogo uravneniya s periodicheskimi koeffitsientami”, Differents. uravneniya, 5:11 (1969), 1990–2001 | MR | Zbl