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

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Abstract

The two-dimensional linear differential system

$$\begin{aligned} x' = y, \quad y' = -x-h(t)y \end{aligned}$$

is considered, where \(h \in C^1[t_0,\infty )\). This system is equivalent to the damped linear oscillator

$$\begin{aligned} x'' + h(t) x' + x = 0. \end{aligned}$$

Necessary and sufficient conditions are established for the length of every nontrivial solution to be finite and infinity.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Science, Okayama University of Science, Ridaichou 1-1, Okayama, 700-0005, Japan

    Masakazu Onitsuka & Satoshi Tanaka

Authors
  1. Masakazu Onitsuka
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  2. Satoshi Tanaka
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Correspondence to Satoshi Tanaka.

Additional information

This work was supported by JSPS KAKENHI Grant Number 26400182.

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Onitsuka, M., Tanaka, S. Rectifiability of Solutions for a Class of Two-Dimensional Linear Differential Systems. Mediterr. J. Math. 14, 51 (2017). https://doi.org/10.1007/s00009-017-0854-5

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  • DOI: https://doi.org/10.1007/s00009-017-0854-5

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