Geodesic
A nonlinear singular eigenvalue problem for a Hamiltonian system of differential equations with redundant condition
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 599-609 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A nonlinear eigenvalue problem for a self-adjoint Hamiltonian system of differential equations is examined on an infinite half-line. It is assumed that the original data (that is, the system matrix and the matrix of boundary conditions) satisfy certain monotonicity conditions for the spectral parameter. In addition to the initial condition and the requirement that the solution be bounded on infinity, a redundant nonlocal condition specified by a Stieltjes integral is imposed. In order to make the resulting problem nontrivially solvable, it is replaced by an auxiliary problem, which is consistent subject to all the above conditions. This auxiliary problem is examined, and a numerical method that solves it is given. 
@article{ZVMMF_2015_55_4_a7,
     author = {A. A. Abramov and L. F. Yukhno},
     title = {A nonlinear singular eigenvalue problem for a {Hamiltonian} system of~differential equations with redundant condition},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {599--609},
     year = {2015},
     volume = {55},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a7/}
}
TY  - JOUR
AU  - A. A. Abramov
AU  - L. F. Yukhno
TI  - A nonlinear singular eigenvalue problem for a Hamiltonian system of differential equations with redundant condition
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 599
EP  - 609
VL  - 55
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a7/
LA  - ru
ID  - ZVMMF_2015_55_4_a7
ER  - 
%0 Journal Article
%A A. A. Abramov
%A L. F. Yukhno
%T A nonlinear singular eigenvalue problem for a Hamiltonian system of differential equations with redundant condition
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 599-609
%V 55
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a7/
%G ru
%F ZVMMF_2015_55_4_a7
A. A. Abramov; L. F. Yukhno. A nonlinear singular eigenvalue problem for a Hamiltonian system of differential equations with redundant condition. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 599-609. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a7/

[1] Abramov A. A., Yukhno L. F., “Reshenie sistemy lineinykh obyknovennykh differentsialnykh uravnenii s izbytochnymi usloviyami”, Zh. vychisl. matem. i matem. fiz., 54:4 (2014), 585–590 | Zbl

[2] Abramov A. A., Ulyanova V. I., Yukhno L. F., “O samosopryazhennoi nelineinoi spektralnoi zadache dlya gamiltonovoi sistemy differentsialnykh uravnenii s osobennostyami”, Zh. vychisl. matem. i matem. fiz., 48:7 (2008), 1202–1208 | MR

[3] Abramov A. A., Yukhno L. F., “Nelineinaya spektralnaya zadacha dlya gamiltonovoi sistemy differentsialnykh uravnenii s izbytochnymi usloviyami”, Differents. ur-niya, 50:7 (2014), 877–883 | Zbl

[4] Abramov A. A., Yukhno L. F., “Reshenie singulyarnoi nelokalnoi zadachi dlya lineinoi sistemy obyknovennykh differentsialnykh uravnenii s izbytochnymi usloviyami”, Zh. vychisl. matem. i matem. fiz., 55:3 (2015), 385–392 | Zbl

[5] Abramov A. A., Konyukhova N. B., “Transfer of admissible boundary conditions from a singular point for systems of linear ordinary differential equations”, Sovjet. J. Numer. Analys. Math. Modelling, 1:4 (1986), 245–265 | MR | Zbl

[6] Abramov A. A., “O chislennom reshenii nekotorykh algebraicheskikh zadach, voznikayuschikh v teorii ustoichivosti”, Zh. vychisl. matem. i matem. fiz., 24:3 (1984), 339–347 | MR | Zbl

[7] Abramov A. A., “Modifikatsiya odnogo metoda resheniya nelineinoi samasopryazhennoi spektralnoi zadachi dlya gamiltonovykh sistem obyknovennykh differentsialnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 51:1 (2011), 39–43 | MR | Zbl