English

Wa\'zewski Topological Principle and V-bounded Solutions of Nonlinear Systems

Classical Analysis and ODEs 2009-01-05 v1 Dynamical Systems

Abstract

We use the Wa\'zewski topological principle to establish a number of new sufficient conditions for the existence of proper (defined on the entire time axis) solutions of essentially nonlinear nonautonomous systems. The systems under consideration are characterized by the monotonicity property with respect to a certain auxiliary guiding function W(t,x)W(t,x) depending on time and phase coordinates. Another auxiliary function V(t,x)V(t,x), which is positively defined in the phase variables xx for any tt, is used to estimate the deviation of the proper solutions from the origin.

Keywords

Cite

@article{arxiv.0901.0234,
  title  = {Wa\'zewski Topological Principle and V-bounded Solutions of Nonlinear Systems},
  author = {Volodymyr Lagoda and Igor Parasyuk},
  journal= {arXiv preprint arXiv:0901.0234},
  year   = {2009}
}

Comments

19 pages

R2 v1 2026-06-21T11:57:08.438Z