Rectifiable and nonrectifiable solution curves of half-linear differential systems

Yuki Naito, Mervan Pašić, Satoshi Tanaka

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We study a geometric kind of asymptotic behaviour of every C1 solution of a class of nonautonomous systems of half-linear differential equations with continuous coefficients. We give necessary and sufficient conditions such that the image of every solution (solution curve) has finite length (rectifiable curve) and infinite length (nonrectifiable, possible fractal curve). A particular attention is paid to systems having attractive zero solution. The main results are proved by using a new result for the nonrectifiable plane curves.

Original languageEnglish
Pages (from-to)575-590
Number of pages16
JournalMathematica Slovaca
Volume68
Issue number3
DOIs
Publication statusPublished - 2018 Jun 26
Externally publishedYes

Keywords

  • asymptotic behaviour
  • attractive zero solution
  • Half-linear system
  • nonrectifiable curve
  • rectifiable curve

ASJC Scopus subject areas

  • Mathematics(all)

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