### Abstract

It is shown that the exponential growth rate of a nonoscillatory solution in a neighborhood of the zero equilibrium of a nonlinear higher order difference equation is often a positive characteristic root of the corresponding linearized equation. The proof is based on Pringsheim's theorem.

Original language | English |
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Pages (from-to) | 1033-1036 |

Number of pages | 4 |

Journal | Journal of Difference Equations and Applications |

Volume | 10 |

Issue number | 11 |

DOIs | |

Publication status | Published - Sep 2004 |

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### Keywords

- Characteristic equation
- Growth rate
- Linearized equation
- Nonlinear difference equation
- Nonoscillatory solution
- Perron-type theorem

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Applied Mathematics

### Cite this

**A note on the growth rates of nonoscillatory solutions of nonlinear difference equations.** / Pituk, M.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A note on the growth rates of nonoscillatory solutions of nonlinear difference equations

AU - Pituk, M.

PY - 2004/9

Y1 - 2004/9

N2 - It is shown that the exponential growth rate of a nonoscillatory solution in a neighborhood of the zero equilibrium of a nonlinear higher order difference equation is often a positive characteristic root of the corresponding linearized equation. The proof is based on Pringsheim's theorem.

AB - It is shown that the exponential growth rate of a nonoscillatory solution in a neighborhood of the zero equilibrium of a nonlinear higher order difference equation is often a positive characteristic root of the corresponding linearized equation. The proof is based on Pringsheim's theorem.

KW - Characteristic equation

KW - Growth rate

KW - Linearized equation

KW - Nonlinear difference equation

KW - Nonoscillatory solution

KW - Perron-type theorem

UR - http://www.scopus.com/inward/record.url?scp=4544280733&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544280733&partnerID=8YFLogxK

U2 - 10.1080/10236190412331285379

DO - 10.1080/10236190412331285379

M3 - Article

AN - SCOPUS:4544280733

VL - 10

SP - 1033

EP - 1036

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

SN - 1023-6198

IS - 11

ER -