### Abstract

The autonomous planar half-linear differential system (Formula Presented.) is considered, where a, b, c and d are real constants, p and p^{∗} are positive numbers with 1/p + 1/p^{∗}= 1 , and ϕ_{q}(s) = |s|^{q} ^{-} ^{2}s for s≠ 0 and ϕ_{q}(0) = 0 , q> 1. When p= 2 , this system is reduced to the linear system (Formula Presented.), which can be solved by eigenvalues of the matrix (Formula Presented.), that is, roots of the characteristic equation (λ- a) (λ- d) - bc= 0. In this paper, the characteristic equation for the autonomous planar half-linear differential system is introduced, and the asymptotic behavior of its solutions is established by roots of the characteristic equation.

Original language | English |
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Pages (from-to) | 336-364 |

Number of pages | 29 |

Journal | Acta Mathematica Hungarica |

Volume | 152 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2017 Aug 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Acta Mathematica Hungarica*,

*152*(2), 336-364. https://doi.org/10.1007/s10474-017-0722-6