Evgeny K. Leinartas, “The criterion of asymptotic stability of a multidimensional differece equation with the constant coefficiens”, J. Sib. Fed. Univ. Math. Phys., 2011, Volume 4, Issue 1,Pages <nobr>112

The criterion of asymptotic stability of a multidimensional differece equation with the constant coefficiens

Evgeny K. Leinartas

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: It is obtained the nessessary condition of the stability of a homogeneous Cauchy problem for a multidimensional difference operator and the criterion of its asymptotic stability in terms connecting with the ameoba of an algebraic hypersurface.

Keywords: Cauchy problem, multidimensional difference operator, ameoba of algebraic hypersurface.

UDC: 517.55

Received: 18.08.2010
Received in revised form: 25.09.2010
Accepted: 30.10.2010