A Perron-type theorem for nonautonomous differential equations with different growth rates

Yongxin Jiang; Can Zhang; Zhaosheng Feng

doi:10.3934/dcdss.2017052

Article Contents

2017, Volume 10, Issue 5: 995-1008. Doi: 10.3934/dcdss.2017052

This issue Previous Article Global Hopf bifurcation of a population model with stage structure and strong Allee effect Next Article Steady states of a Sel'kov-Schnakenberg reaction-diffusion system

A Perron-type theorem for nonautonomous differential equations with different growth rates

1.
Department of Mathematics, College of Science, Hohai University, Nanjing, Jiangsu 210098, China
2.
School of Mathematical and Statistical Sciences, University of Texas-Rio Grande valley, Edinburg, Texas 78539, USA

^* Corresponding author: Yongxin Jiang
^* Corresponding author: Yongxin Jiang

Received: January 1, 2016

Revised: February 1, 2017

Published online: October 1, 2017

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Abstract

We show that if the Lyapunov exponents associated to a linear equation $x'=A(t)x$ are equal to the given limits, then this asymptotic behavior can be reproduced by the solutions of the nonlinear equation $x'=A(t)x+f(t, x)$ for any sufficiently small perturbation $f$. We consider the linear equation with a very general nonuniform behavior which has different growth rates.

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Mathematics Subject Classification: Primary: 34D08, 34D10.

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References

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