Volodymyr Lagoda | Searcharxiv

arXiv2010

Existence of V-bounded solutions for nonautonomous nonlinear systems via the Wazewski topological principle

We establish a number of new sufficient conditions for the existence of global (defined on the entire time axis) solutions of nonlinear nonautonomous systems by means of the Wazewski topological principle. The systems under consideration are characterized by the monotonicity property with respect to a certain auxiliary guiding function W(t,x) depending on time and phase coordinates. Another auxiliary spatially coercive function V(t,x) is used to estimate the location of global solutions in the extended phase space. The approach developed is applied to Lagrangian systems, and in particular, to establish new sufficient conditions for the existence of almost periodic solutions.

math.CA↗

arXiv2009

Waźewski Topological Principle and V-bounded Solutions of Nonlinear Systems

We use the Waźewski 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 $W(t,x)$ depending on time and phase coordinates. Another auxiliary function $V(t,x)$, which is positively defined in the phase variables $x$ for any $t$, is used to estimate the deviation of the proper solutions from the origin.

math.CA↗