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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 3
  • Publication Date: 2020
  • Title of Journal : CARPATHIAN JOURNAL OF MATHEMATICS
  • Page Numbers: pp.341-349
  • Keywords: oscillations, strongly unpredictable perturbations, strongly unpredictable solutions, unpredictable solutions, asymptotical stability, POINCARE CHAOS

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.