Dynamics of solutions of the simplest nonlinear boundary-value problems

  • O. Yu. Romanenko
  • O. M. Sharkovsky

Abstract

We investigate two classes of essentially nonlinear boundary-value problems by using methods of the theory of dynamical systems and two special metrics. We prove that, for boundary-value problems of both these classes, all solutions tend (in the first metric) to upper semicontinuous functions and, under sufficiently general conditions, the asymptotic behavior of almost every solution can be described (by using the second metric) by a certain stochastic process.
Published
25.06.1999
How to Cite
RomanenkoO. Y., and SharkovskyO. M. “Dynamics of Solutions of the Simplest Nonlinear Boundary-Value Problems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 6, June 1999, pp. 810–826, https://umj.imath.kiev.ua/index.php/umj/article/view/4668.
Section
Research articles