کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9501573 | 1338751 | 2005 | 45 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Stability of nonautonomous differential equations in Hilbert spaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Stability of nonautonomous differential equations in Hilbert spaces Stability of nonautonomous differential equations in Hilbert spaces](/preview/png/9501573.png)
چکیده انگلیسی
We introduce a large class of nonautonomous linear differential equations vâ²=A(t)v in Hilbert spaces, for which the asymptotic stability of the zero solution, with all Lyapunov exponents of the linear equation negative, persists in vâ²=A(t)v+f(t,v) under sufficiently small perturbations f. This class of equations, which we call Lyapunov regular, is introduced here inspired in the classical regularity theory of Lyapunov developed for finite-dimensional spaces, that is nowadays apparently overlooked in the theory of differential equations. Our study is based on a detailed analysis of the Lyapunov exponents. Essentially, the equation vâ²=A(t)v is Lyapunov regular if for every k the limit of Î(t)1/t as tââ exists, where Î(t) is any k-volume defined by solutions v1(t),â¦,vk(t). We note that the class of Lyapunov regular linear equations is much larger than the class of uniformly asymptotically stable equations.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 217, Issue 1, 1 October 2005, Pages 204-248
Journal: Journal of Differential Equations - Volume 217, Issue 1, 1 October 2005, Pages 204-248
نویسندگان
Luis Barreira, Claudia Valls,