In this paper we introduce a cone invariance property, which ensures dichotomy for a linear differential system under suitable technical conditions. This property consists in the existence of two disjoint cones, such that the forward (backward) flow originating from a plane that lies in the first (second) cone remains in the cone itself. This property can be verified even if the system matrix is not diagonal dominant. As a consequence, the resulting conditions for dichotomy are not related to diagonal dominance and can be applied to cases in which some of the classical hypotheses appearing in literature do not hold.
A sufficient condition for dichotomy based on a suitable invariance property / Consolini, Luca; Tosques, Mario. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 251:6(2011), pp. 1475-1488. [10.1016/j.jde.2011.05.028]
A sufficient condition for dichotomy based on a suitable invariance property
CONSOLINI, Luca;TOSQUES, Mario
2011-01-01
Abstract
In this paper we introduce a cone invariance property, which ensures dichotomy for a linear differential system under suitable technical conditions. This property consists in the existence of two disjoint cones, such that the forward (backward) flow originating from a plane that lies in the first (second) cone remains in the cone itself. This property can be verified even if the system matrix is not diagonal dominant. As a consequence, the resulting conditions for dichotomy are not related to diagonal dominance and can be applied to cases in which some of the classical hypotheses appearing in literature do not hold.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
