### Abstract

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.

Original language | English |
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Pages (from-to) | 89-111 |

Number of pages | 23 |

Journal | Applied Mathematics and Computation |

Volume | 36 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1990 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

### Cite this

**Sharp conditions for existence of nontrivial invariant cones of nonnegative initial values of difference equations.** / Győri, I.

Research output: Contribution to journal › Article

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TY - JOUR

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

AU - Győri, I.

PY - 1990

Y1 - 1990

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.

UR - http://www.scopus.com/inward/record.url?scp=38249020665&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249020665&partnerID=8YFLogxK

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 -