Geodesic
Necessary conditions for the system of two second degree differential equations to have Painlev\'e property
Problemy fiziki, matematiki i tehniki, no. 2 (2018), pp. 69-75

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Necessary conditions for the system in the title to be Painlevé type system were given.
Keywords: system of the ordinary differential equations, Painleve's property, movable critical singularities, method of small parameter. 
@article{PFMT_2018_2_a9,
     author = {V. M. Petsevich and V. A. Pronko},
     title = {Necessary conditions for the system of two second degree differential equations to have {Painlev\'e} property},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {69--75},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2018_2_a9/}
}
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V. M. Petsevich; V. A. Pronko. Necessary conditions for the system of two second degree differential equations to have Painlev\'e property. Problemy fiziki, matematiki i tehniki, no. 2 (2018), pp. 69-75. http://geodesic.mathdoc.fr/item/PFMT_2018_2_a9/