TY - JOUR

T1 - Sharp conditions for existence of nontrivial invariant cones of nonnegative initial values of difference equations

AU - Györi, Istvan

PY - 1990/3

Y1 - 1990/3

N2 - It is proved that an arbitrary scalar difference equation has a nontrivial invariant cone in the set of the nonnegative initial values if and only if the associated characteristic equation has a positive root. By using this fact, there is given a construction of the maximal invariant cone in the set of nonnegative initial values via a positive root of the associated characteristic equation. Finally, the present results are compared with some earlier ones which were obtained for delay differential equations in the same direction.

AB - It is proved that an arbitrary scalar difference equation has a nontrivial invariant cone in the set of the nonnegative initial values if and only if the associated characteristic equation has a positive root. By using this fact, there is given a construction of the maximal invariant cone in the set of nonnegative initial values via a positive root of the associated characteristic equation. Finally, the present results are compared with some earlier ones which were obtained for delay differential equations in the same direction.

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U2 - 10.1016/0096-3003(90)90014-T

DO - 10.1016/0096-3003(90)90014-T

M3 - Article

AN - SCOPUS:38249020665

VL - 36

SP - 89

EP - 111

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 2

ER -