Spectral theory for linear non-autonomous differential equations
type: Item
instance of: scholarly article
title: Spectral theory for linear non-autonomous differential equations
zbMATH Open document ID: 0811.34064
author: Nguyen Van Minh
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-12-14T00:00:00Z
review text: The linear non-autonomous equations \(x' = A(t)x\) having bounded growth and decay are considered \((A(t)\) is a matrix function). The spectral mapping theorem \(\sigma (T^ h) = \exp h \sigma' (L)\) and rotational invariance are proved by introducing a semigroup of the operators \(T^ h\) using the relations \((T^ hv)(t) = X(t,t-h) v(t-h)\) and \(\lim v(t) = 0\) as \(t \to \infty\). As examples the difference equation \(x(t) = Bx(t-1) + f(t)\), the linearly perturbed equation \(dy/dt = (A(t) + B(t))y\), the equation \(dx/dt = Ax\) where \(A\) is a matrix and the Sacker-Sell spectrum are discussed.
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 703331
zbMATH Keywords: linear non-autonomous equations
zbMATH Keywords: spectral mapping theorem
zbMATH Keywords: rotational invariance
zbMATH Keywords: semigroup
zbMATH Keywords: difference equation
zbMATH Keywords: linearly perturbed equation
zbMATH Keywords: Sacker-Sell spectrum
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1360
OpenAlex ID: W2073099260
DOI: 10.1006/JMAA.1994.1360
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description: scientific article; zbMATH DE number 703331