Quasilinear differential equations with strongly unpredictable solutions

AKHMET M., Tleubergenova M., Zhamanshin A.

CARPATHIAN JOURNAL OF MATHEMATICS, vol.36, no.3, pp.341-349, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 3
  • Publication Date: 2020
  • Journal Name: CARPATHIAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.341-349
  • Keywords: oscillations, strongly unpredictable perturbations, strongly unpredictable solutions, unpredictable solutions, asymptotical stability, POINCARE CHAOS
  • Middle East Technical University Affiliated: Yes

Abstract

The authors discuss the existence and uniqueness of asymptotically stable unpredictable solutions for some quasilinear differential equations. Two principal novelties are in the basis of this research. The first one is that all coordinates of the solution are unpredictable functions. That is, solutions are strongly unpredictable. Secondly, perturbations are strongly unpredictable functions in the time variable. Examples with numerical simulations are presented to illustrate the theoretical results.