I. P. Martynov, O. N. Parmanchuk, V. M. Pecevich, “On a cross system of two differential equations with the Painleve property”, PFMT, 2011, Issue 3(8),Pages <nobr>74

MATHEMATICS

On a cross system of two differential equations with the Painleve property

I. P. Martynov, O. N. Parmanchuk, V. M. Pecevich

Y. Kupala Grodno State University, Grodno

Abstract: 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, singular solution, test of Painleve, resonances.

UDC: 517.925

Received: 06.06.2011