TY - JOUR

T1 - Characteristic equation for autonomous planar half-linear differential systems

AU - Onitsuka, M.

AU - Tanaka, S.

N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Number 26400182.
Publisher Copyright:
© 2017, Akadémiai Kiadó, Budapest, Hungary.

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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 ϕq(s) = |s|q - 2s for s≠ 0 and ϕq(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.

AB - 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 ϕq(s) = |s|q - 2s for s≠ 0 and ϕq(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.

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U2 - 10.1007/s10474-017-0722-6

DO - 10.1007/s10474-017-0722-6

M3 - Article

AN - SCOPUS:85019854188

SN - 0236-5294

VL - 152

SP - 336

EP - 364

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 2

ER -