Geodesic
On unimprovable conditions of the solvability of the periodic problem for second order functional differential equations
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2013), pp. 3-19
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Necessary and sufficient conditions for the unique solvability of the periodic boundary value problem for all linear second order functional differential equations with the given norm of the functional operators.
Keywords: linear equations with delay, periodic boundary value problem, periodic solutions, functional differential equations. 
@article{VUU_2013_3_a0,
     author = {E. I. Bravyi},
     title = {On unimprovable conditions of the solvability of the periodic problem for second order functional differential equations},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {3--19},
     year = {2013},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2013_3_a0/}
}
TY  - JOUR
AU  - E. I. Bravyi
TI  - On unimprovable conditions of the solvability of the periodic problem for second order functional differential equations
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2013
SP  - 3
EP  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VUU_2013_3_a0/
LA  - ru
ID  - VUU_2013_3_a0
ER  - 
%0 Journal Article
%A E. I. Bravyi
%T On unimprovable conditions of the solvability of the periodic problem for second order functional differential equations
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2013
%P 3-19
%N 3
%U http://geodesic.mathdoc.fr/item/VUU_2013_3_a0/
%G ru
%F VUU_2013_3_a0
E. I. Bravyi. On unimprovable conditions of the solvability of the periodic problem for second order functional differential equations. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2013), pp. 3-19. http://geodesic.mathdoc.fr/item/VUU_2013_3_a0/

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

[2] Komlenko Yu. V., Tonkov E. L., “The periodic boundary value problem for a second order ordinary differential equation”, Dokl. Akad. Nauk SSSR, 179:1 (1968), 17–19 | MR | Zbl

[3] Cabada A., Cid J. A., “On the sign of the Green's function associated to Hill's equation with an indefinite potential”, Appl. Math. Comput., 205:1 (2008), 303–308 | DOI | MR | Zbl

[4] Hakl R., Torres P. J., “Maximum and antimaximum principles for a second order differential operator with variable coefficients of indefinite sign”, Appl. Math. Comput., 217:19 (2011), 7599–7611 | DOI | MR | Zbl

[5] Lomtatidze A., Mukhigulashvili S., “On periodic solutions of second order functional differential equations”, Mem. Differential Equations Math. Phys., 5 (1995), 125–126 | Zbl

[6] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Introduction to the theory of functional differential equations, Nauka, Moscow, 1991, 280 pp. | MR | Zbl

[7] Hakl R., Mukhigulashvili S., “A periodic boundary value problem for functional differential equations of higher order”, Georgian Math. J., 16:4 (2009), 651–665 | MR | Zbl

[8] Bravyi E. I., “On the best constants in the solvability conditions for the periodic boundary value problem for higher-order functional differential equations”, Differ. Uravn., 48:6 (2012), 773–780 | MR | Zbl

[9] Bravyi E. I., The solvability of boundary value problems for linear functional differential equations, Regular Chaotic Dynamics, Moscow–Izhevsk, 2011, 372 pp.

[10] Bravyi E. I., “On the solvability of the periodic boundary value problem for a linear functional differential equation”, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2009, no. 3, 12–24