Geodesic
On a cross system of two differential equations with the Painleve property
Problemy fiziki, matematiki i tehniki, no. 3 (2011), pp. 74-77 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article deals with the cross-system of two differential equations of the second degree and third-degree derivative of the variables. The necessary and sufficient conditions having the Painleve property for solutions of this system are obtained.
Keywords: cross system of differential equations, property of Painleve, test of Painleve, resonances.
Mots-clés : singular solution 
@article{PFMT_2011_3_a11,
     author = {I. P. Martynov and O. N. Parmanchuk and V. M. Pecevich},
     title = {On a cross system of two differential equations with the {Painleve} property},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {74--77},
     year = {2011},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2011_3_a11/}
}
TY  - JOUR
AU  - I. P. Martynov
AU  - O. N. Parmanchuk
AU  - V. M. Pecevich
TI  - On a cross system of two differential equations with the Painleve property
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2011
SP  - 74
EP  - 77
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/PFMT_2011_3_a11/
LA  - ru
ID  - PFMT_2011_3_a11
ER  - 
%0 Journal Article
%A I. P. Martynov
%A O. N. Parmanchuk
%A V. M. Pecevich
%T On a cross system of two differential equations with the Painleve property
%J Problemy fiziki, matematiki i tehniki
%D 2011
%P 74-77
%N 3
%U http://geodesic.mathdoc.fr/item/PFMT_2011_3_a11/
%G ru
%F PFMT_2011_3_a11
I. P. Martynov; O. N. Parmanchuk; V. M. Pecevich. On a cross system of two differential equations with the Painleve property. Problemy fiziki, matematiki i tehniki, no. 3 (2011), pp. 74-77. http://geodesic.mathdoc.fr/item/PFMT_2011_3_a11/

[1] O. N. Parmanchuk, V. M. Petsevich, V. A. Pronko, “Ob odnoi perekrestnoi sisteme dvukh differentsialnykh uravnenii pervogo poryadka i vtoroi stepeni so svoistvom Penleve”, Vestnik GrGU. Seriya 2. Matematika, fizika, informatika, vychislitelnaya tekhnika i upravlenie, biologiya, 2008, no. 3, 72–79

[2] I. P. Martynov, O. N. Parmanchuk, V. M. Petsevich, “Ob odnoi sisteme dvukh differentsialnykh uravnenii vtoroi stepeni so svoistvom Penleve”, Vestnik GrGU. Seriya 2. Matematika, fizika, informatika, vychislitelnaya tekhnika i upravlenie, biologiya, 2010, no. 2, 9–17

[3] O. N. Parmanchuk, “Analiticheskie svoistva reshenii odnoi perekrestnoi sistemy dvukh differentsialnykh uravnenii”, Vestnik GrGU. Seriya 2. Matematika, fizika, informatika, vychislitelnaya tekhnika i upravlenie, biologiya, 2011, no. 2, 35–41

[4] N. S. Berezkina, I. P. Martynov, V. A. Pronko, “O sisteme dvukh drobno-lineinykh differentsialnykh uravnenii stepeni $n$ so svoistvom Penleve”, Differentsialnye uravneniya, 42:4 (2006), 1–6 | MR

[5] E. L. Ains, Obyknovennye differentsialnye uravneniya, Kharkov, 1939, 718 pp.

[6] C. Cosgrove, G. Scoufis, “Painleve classification of a class of differential equations of the second order and second degree”, Stud. Appl. Math., 88 (1993), 25–87 | MR | Zbl

[7] T. N. Vankova i dr., “O nekotorykh analiticheskikh svoistvakh reshenii algebraicheskikh differentsialnykh uravnenii”, Vestnik GrGU. Seriya 2. Matematika, fizika, informatika, vychislitelnaya tekhnika i upravlenie, biologiya, 2008, no. 1, 8–16

[8] V. V. Golubev, Lektsii po analiticheskoi teorii differentsialnykh uravnenii, GITTL, M.–L., 1950, 436 pp.