Generalized Lyapunov functions and functional equations

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1965 English Publisher:Springer Science and Business Media LLCJournal:Annali di Matematica Pura ed Applicata, volume 69, pages 305-320 (issn: 0373-3114, eissn: 1618-1891,

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Authors: Hartman, Philip;

doi: 10.1007/bf02414376

Generalized Lyapunov functions and functional equations

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Abstract

Some results of Minty and Browder on the existence of solutions of functional equations are generalized by replacing the notion of monotony by one involving a Lyapunov function. In the last section, analogous arguments are used to obtain an existence theorem for an initial value problem belonging to an ordinary differential equation on Hilbert space.

Keywords

ordinary differential equations, Stability theory for ordinary differential equations, Functional equations and inequalities

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