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

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

2009-11-24

arxiv.org/abs/0911.4643v3

Mathematics

Classical Analysis and ODEs

34 pages; corrected typos; first sentence in the proof of Theorem 1 has been removed

Scientific paper

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.

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