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Frequency tests for the existence of boundary solutions

Frequency tests for the existence of boundary solutions ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 7, pp. 916–924.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c A.I. Perov, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 7, pp. 896–904. ORDINARY DIFFERENTIAL EQUATIONS Frequency Tests for the Existence of Boundary Solutions A. I. Perov Voronezh State University, Voronezh, Russia Received November 9, 2005 DOI: 10.1134/S001226610707004X Consider the quasilinear system of ordinary differential equations x ˙ = Ax + f (t, x), (1) n n where ˙ = d/dt, x is an n-vector, A is a constant n × n matrix, and f (t, x): R × C → C is some vector function. The complex space C is considered with the standard inner product and with the 1/2 norm x =(x, x) . We are interested in bounded solutions of system (1). Throughout the following, we assume that Re λ =0, ... , Re λ =0, (2) 1 n where λ ,... ,λ is the complete set of eigenvalues of the matrix A; i.e., the spectrum of the matrix 1 n A has an empty intersection with the imaginary axis. This assumption is necessarily true if Re λ < 0, ... , Re http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Frequency tests for the existence of boundary solutions

Perov, A.
Differential Equations , Volume 43 (7) – Oct 2, 2007
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References (3)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S001226610707004X
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 7, pp. 916–924.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c A.I. Perov, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 7, pp. 896–904. ORDINARY DIFFERENTIAL EQUATIONS Frequency Tests for the Existence of Boundary Solutions A. I. Perov Voronezh State University, Voronezh, Russia Received November 9, 2005 DOI: 10.1134/S001226610707004X Consider the quasilinear system of ordinary differential equations x ˙ = Ax + f (t, x), (1) n n where ˙ = d/dt, x is an n-vector, A is a constant n × n matrix, and f (t, x): R × C → C is some vector function. The complex space C is considered with the standard inner product and with the 1/2 norm x =(x, x) . We are interested in bounded solutions of system (1). Throughout the following, we assume that Re λ =0, ... , Re λ =0, (2) 1 n where λ ,... ,λ is the complete set of eigenvalues of the matrix A; i.e., the spectrum of the matrix 1 n A has an empty intersection with the imaginary axis. This assumption is necessarily true if Re λ < 0, ... , Re

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Differential Equations – Springer Journals

Published: Oct 2, 2007

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