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 depending on time and phase coordinates. Another auxiliary function , which is positively defined in the phase variables for any , is used to estimate the deviation of the proper solutions from the origin.
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