Geodesic
Nonzero solutions to a~two-point boundary-value periodic problem for differential equations with maxima
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2010), pp. 52-63.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove a theorem on the unique existence of a solution to a nonlinear equation with maxima and demonstrate its continuous dependence on the initial function and the parameter of the problem. We also establish conditions for the existence of a nonzero solution to a two-point boundary-value periodic problem in dependence of both linear and nonlinear terms of the equation.
Keywords: initial function, parameter, compact, equation with maxima, two-point boundary-value periodic problem, fundamental matrix, operator, fixed point, admissible vector of a matrix.
Mots-clés : theorem on the unique existence of a solution 
@article{IVM_2010_6_a5,
     author = {M. T. Teryokhin and V. V. Kiryushkin},
     title = {Nonzero solutions to a~two-point boundary-value periodic problem for differential equations with maxima},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {52--63},
     publisher = {mathdoc},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_6_a5/}
}
TY  - JOUR
AU  - M. T. Teryokhin
AU  - V. V. Kiryushkin
TI  - Nonzero solutions to a~two-point boundary-value periodic problem for differential equations with maxima
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 52
EP  - 63
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_6_a5/
LA  - ru
ID  - IVM_2010_6_a5
ER  - 
%0 Journal Article
%A M. T. Teryokhin
%A V. V. Kiryushkin
%T Nonzero solutions to a~two-point boundary-value periodic problem for differential equations with maxima
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 52-63
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2010_6_a5/
%G ru
%F IVM_2010_6_a5
M. T. Teryokhin; V. V. Kiryushkin. Nonzero solutions to a~two-point boundary-value periodic problem for differential equations with maxima. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2010), pp. 52-63. http://geodesic.mathdoc.fr/item/IVM_2010_6_a5/

[1] Azbelev N. V., Ermolaev M. B., Simonov P. M., “K voprosu ob ustoichivosti funktsionalno-differentsialnykh uravnenii po pervomu priblizheniyu”, Izv. vuzov. Matematika, 1995, no. 10, 3–9 | MR | Zbl

[2] Azbelev N. V., Simonov P. M., “Funktsionalno-differentsialnye uravneniya i teoriya ustoichivosti uravnenii s posledeistviem”, Vestn. PGTU. Funkts.-differents. uravneniya, 2002, 52–69

[3] Ermolaev M. B., Ustoichivost reshenii nekotorykh klassov suschestvenno nelineinykh funktsionalno-differentsialnykh uravnenii, Diss. $\dots$ kand. fiz.-matem. nauk, Izhevsk, 1995

[4] Magomedov A. R., Nabiev G. M., “O nekotorykh voprosakh ustoichivosti reshenii lineinykh differentsialnykh uravnenii s maksimumami”, DAN AzSSR, 42:2 (1986), 3–6 | MR | Zbl

[5] Bainov D. D., Voulov H. D., Differential equations with maximum: stability of solutions, Sofia, 1992, 100 pp.

[6] Petukhov A. R., “Voprosy kachestvennogo issledovaniya reshenii uravnenii s maksimumami”, Izv. vuzov. Matematika, 1964, no. 4, 116–119 | MR | Zbl

[7] Magomedov A. R., Ryabov Yu. A., “O periodicheskikh resheniyakh nelineinykh differentsialnykh uravnenii s maksimumami”, Izv. AN AzSSR. Ser. fiz.-tekh. i matem. nauk, 1975, no. 2, 76–83 | MR | Zbl

[8] Magomedov A. R., Ryabov Yu. A., Differentsialnye uravneniya s maksimumami, In-t Kosm. issled. AN AzSSR, Baku, 1964, 42 pp.

[9] Magomedov A. R., “O nekotorykh voprosakh differentsialnykh uravnenii s maksimumami”, Izv. AN AzSSR. Ser. fiz.-tekh. i matem. nauk, 1977, no. 1, 104–108 | MR | Zbl

[10] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Vvedenie v teoriyu funktsionalno-differentsialnykh uravnenii, Nauka, M., 1991, 278 pp. | MR | Zbl

[11] Maksimov V. P., Voprosy obschei teorii funktsionalno-differentsialnykh uravnenii. Izbrannye trudy, Izd-vo PGU, PSI, PSSGK, Perm, 2003, 306 pp.

[12] Koddington E. A., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii, In. lit., M., 1958, 475 pp.