### Abstract

We establish the existence of periodic solution of a class of non-autonomous second-order systems, over(x, ̈) + μ x + V (t, x) = 0, where V (t, x) = (v_{1} (t, x), ..., v_{n} (t, x)), if lim_{| x | → ∞} frac(v_{i} (t, x), | x |) = 0, i = 1, ..., n, uniformly in t and V is bounded below or above for appropriate ranges of μ.

Original language | English (US) |
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Pages (from-to) | 1271-1275 |

Number of pages | 5 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 71 |

Issue number | 3-4 |

DOIs | |

State | Published - Aug 1 2009 |

### Fingerprint

### Keywords

- Cone
- Fixed point theorem
- Non-autonomous system
- Periodic solutions

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**Periodic solutions to non-autonomous second-order systems.** / Wang, Haiyan.

Research output: Contribution to journal › Article

*Nonlinear Analysis, Theory, Methods and Applications*, vol. 71, no. 3-4, pp. 1271-1275. https://doi.org/10.1016/j.na.2008.11.079

}

TY - JOUR

T1 - Periodic solutions to non-autonomous second-order systems

AU - Wang, Haiyan

PY - 2009/8/1

Y1 - 2009/8/1

N2 - We establish the existence of periodic solution of a class of non-autonomous second-order systems, over(x, ̈) + μ x + V (t, x) = 0, where V (t, x) = (v1 (t, x), ..., vn (t, x)), if lim| x | → ∞ frac(vi (t, x), | x |) = 0, i = 1, ..., n, uniformly in t and V is bounded below or above for appropriate ranges of μ.

AB - We establish the existence of periodic solution of a class of non-autonomous second-order systems, over(x, ̈) + μ x + V (t, x) = 0, where V (t, x) = (v1 (t, x), ..., vn (t, x)), if lim| x | → ∞ frac(vi (t, x), | x |) = 0, i = 1, ..., n, uniformly in t and V is bounded below or above for appropriate ranges of μ.

KW - Cone

KW - Fixed point theorem

KW - Non-autonomous system

KW - Periodic solutions

UR - http://www.scopus.com/inward/record.url?scp=67349167989&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349167989&partnerID=8YFLogxK

U2 - 10.1016/j.na.2008.11.079

DO - 10.1016/j.na.2008.11.079

M3 - Article

AN - SCOPUS:67349167989

VL - 71

SP - 1271

EP - 1275

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 3-4

ER -