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- Title
RECTIFIABLE AND NONRECTIFIABLE SOLUTION CURVES OF HALF-LINEAR DIFFERENTIAL SYSTEMS.
- Authors
YUKI NAITO; PAŠIĆ, MERVAN; SATOSHI TANAKA
- 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.
- Subjects
CURVE rectification &; quadrature; LINEAR differential equations; ASYMPTOTIC theory of algebraic ideals; DIFFERENTIAL equations; PLANE curves; NUMERICAL solutions to difference equations
- Publication
Mathematica Slovaca, 2018, Vol 68, Issue 3, p575
- ISSN
0139-9918
- Publication type
Article
- DOI
10.1515/ms-2017-0126