Geodesic
On the number of solutions for a certain class of nonlinear second-order boundary-value problems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 32-41.

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

The boundary-value problem for the differential equation with quadratic nonlinearity $x''=-ax+b x^2$ with the boundary conditions $x'(0)=x'(T)=0$ is is considered. The number of solutions of for the boundary-value problem is found. An illustrative example is presented.
Keywords: boundary-value problem, quadratic nonlinearity, phase trajectory, multiplicity of solutions, Jacobian elliptic function. 
@article{INTO_2019_160_a4,
     author = {A. V. Kirichuka and F. Zh. Sadyrbaev},
     title = {On the number of solutions for a certain class of nonlinear second-order boundary-value problems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {32--41},
     publisher = {mathdoc},
     volume = {160},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_160_a4/}
}
TY  - JOUR
AU  - A. V. Kirichuka
AU  - F. Zh. Sadyrbaev
TI  - On the number of solutions for a certain class of nonlinear second-order boundary-value problems
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 32
EP  - 41
VL  - 160
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_160_a4/
LA  - ru
ID  - INTO_2019_160_a4
ER  - 
%0 Journal Article
%A A. V. Kirichuka
%A F. Zh. Sadyrbaev
%T On the number of solutions for a certain class of nonlinear second-order boundary-value problems
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 32-41
%V 160
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_160_a4/
%G ru
%F INTO_2019_160_a4
A. V. Kirichuka; F. Zh. Sadyrbaev. On the number of solutions for a certain class of nonlinear second-order boundary-value problems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 32-41. http://geodesic.mathdoc.fr/item/INTO_2019_160_a4/

[1] Konyukhova N. B., Sheina A. A., “Ob odnoi vspomogatelnoi nelineinoi kraevoi zadache v teorii sverkhprovodimosti Ginzburga—Landau i ee mnozhestvennykh resheniyakh”, Vestn. RUDN. Ser. Mat. Inform. Fiz., 3 (2016), 5–20

[2] Kuznetsov A. P., Kuznetsov S. P., Ryskin N. M., Nelineinye kolebaniya, Fizmatlit, M., 2002

[3] Miln-Tomson L., “Ellipticheskie funktsii Yakobi i teta-funktsii”, Spravochnik po spetsialnym funktsiyam, Gl. 16, eds. Abramovits M., Stigan I., Nauka, M., 1979

[4] Uitteker E. T., Vatson Dzh. N., Kurs sovremennogo analiza, Gl. red. fiz.-mat. lit, M., 1963

[5] Ginzburg V. L., “Nobel Lecture: On superconductivity and superfluidity (what I have and have not managed to do) as well as on the “physical minimum” at the beginning of the XXI century”, Rev. Mod. Phys., 76:3 (2004), 981–998 | DOI | MR

[6] Kirichuka A., “The number of solutions to the Neumann problem for the second order differential equation with cubic nonlinearity”, Proc. IMCS Univ. Latv., 17 (2017), 44–51