Necessary and sufficient conditions for the invertibility of the non-linear difference operator $ (\mathscr Dx)(t)=x(t+1)-f(x(t))$ in the space of bounded continuous functions on the real axis

Slyusarchuk, Vasilii Efimovich

doi:10.1070/sm2001v192n04abeh000559

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Cited by 2 publications

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“…We shall not mention here another interesting approaches in studying the existence problem of bounded solutions to nonlinear systems, because they have not been used in this paper. For the corresponding information the reader is referred to [16,17,18,19,20,21,22,23,24,25,26,27,28].…”

Section: Introductionmentioning

confidence: 99%

Waźewski Topological Principle and V-bounded Solutions of Nonlinear Systems

Lagoda,

Parasyuk

2009

Preprint

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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.

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