Rectifiability of Solutions for a Class of Two-Dimensional Linear Differential Systems

Masakazu Onitsuka; Satoshi Tanaka

doi:10.1007/s00009-017-0854-5

Rectifiability of Solutions for a Class of Two-Dimensional Linear Differential Systems

Masakazu Onitsuka, Satoshi Tanaka

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The two-dimensional linear differential system x′=y, y′=-x-h(t)y is considered, where h∈ C¹[ t₀, ∞). This system is equivalent to the damped linear oscillator x″ + h(t)x′ + x=0. Necessary and sufficient conditions are established for the length of every nontrivial solution to be finite and infinity.

Original language	English
Article number	51
Journal	Mediterranean Journal of Mathematics
Volume	14
Issue number	2
DOIs	https://doi.org/10.1007/s00009-017-0854-5
Publication status	Published - 2017 Apr 1
Externally published	Yes

Keywords

Linear system
attractive
nonrectifiable
rectifiable
zero solution

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00009-017-0854-5

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abstract = "The two-dimensional linear differential system x′=y, y′=-x-h(t)y is considered, where h∈ C1[ t0, ∞). This system is equivalent to the damped linear oscillator x″ + h(t)x′ + x=0. Necessary and sufficient conditions are established for the length of every nontrivial solution to be finite and infinity.",

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author = "Masakazu Onitsuka and Satoshi Tanaka",

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AU - Tanaka, Satoshi

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N2 - The two-dimensional linear differential system x′=y, y′=-x-h(t)y is considered, where h∈ C1[ t0, ∞). This system is equivalent to the damped linear oscillator x″ + h(t)x′ + x=0. Necessary and sufficient conditions are established for the length of every nontrivial solution to be finite and infinity.

AB - The two-dimensional linear differential system x′=y, y′=-x-h(t)y is considered, where h∈ C1[ t0, ∞). This system is equivalent to the damped linear oscillator x″ + h(t)x′ + x=0. Necessary and sufficient conditions are established for the length of every nontrivial solution to be finite and infinity.

KW - Linear system

KW - attractive

KW - nonrectifiable

KW - rectifiable

KW - zero solution

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ER -

Rectifiability of Solutions for a Class of Two-Dimensional Linear Differential Systems

Abstract

Keywords

ASJC Scopus subject areas

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