Geodesic
Behavior of stabilizing solutions of the Riccati equation
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 31 (2016) no. 31, pp. 110-133 
V. V. Palin; E. V. Radkevich. Behavior of stabilizing solutions of the Riccati equation. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 31 (2016) no. 31, pp. 110-133. http://geodesic.mathdoc.fr/item/TSP_2016_31_31_a5/
@article{TSP_2016_31_31_a5,
     author = {V. V. Palin and E. V. Radkevich},
     title = {Behavior of stabilizing solutions of the {Riccati} equation},
     journal = {Trudy Seminara im. I.G. Petrovskogo},
     pages = {110--133},
     year = {2016},
     volume = {31},
     number = {31},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TSP_2016_31_31_a5/}
}
TY  - JOUR
AU  - V. V. Palin
AU  - E. V. Radkevich
TI  - Behavior of stabilizing solutions of the Riccati equation
JO  - Trudy Seminara im. I.G. Petrovskogo
PY  - 2016
SP  - 110
EP  - 133
VL  - 31
IS  - 31
UR  - http://geodesic.mathdoc.fr/item/TSP_2016_31_31_a5/
LA  - ru
ID  - TSP_2016_31_31_a5
ER  - 
%0 Journal Article
%A V. V. Palin
%A E. V. Radkevich
%T Behavior of stabilizing solutions of the Riccati equation
%J Trudy Seminara im. I.G. Petrovskogo
%D 2016
%P 110-133
%V 31
%N 31
%U http://geodesic.mathdoc.fr/item/TSP_2016_31_31_a5/
%G ru
%F TSP_2016_31_31_a5

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Sufficient conditions are found for the existence of stabilizing solutions of the Riccati differential equation $y'=\bigl(y-y_1(x)\bigr)\bigl(y-y_2(x)\bigr)$ with given $y_1(x)$ and $y_2(x)$. For various types of stabilizing solutions, the number of points of extremum is examined.

[1] Vasilev V. A., Romanovskii Yu. M., Yakhno V. G., Avtovolnovye protsessy, Nauka, M., 1987

[2] Laks P. D., Giperbolicheskie differentsialnye uravneniya v chastnykh proizvodnykh, NITs «Regulyarnaya i khaoticheskaya dinamika», Izhevskii institut kompyuternykh issledovanii, M.–Izhevsk, 2010

[3] Evans L. K., Uravneniya s chastnymi proizvodnymi, Universitetskaya ser., 7, Tamara Rozhkovskaya, Novosibirsk, 1998

[4] Lukashev E. A., Palin V. V., Radkevich E. V., Yakovlev N. N., “Nonclassical regularization of the multicomponent Euler system”, J. Math. Sci., 196:3 (2014), 322–345 | DOI | MR | Zbl

[5] Filippov A. F., Vvedenie v teoriyu differentsialnykh uravnenii, URSS, M., 2004

[6] Pliss V. A., Nekotorye problemy teorii ustoichivosti v tselom, Izd-vo Leningrad. un-ta, L., 1958