Existence and uniqueness results for Liénard́s equation having a dead band

Allan Sandqvist, Kurt Munk Andersen

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    Abstract

    In the first part of the present paper we consider general systems of first-order autonomous differential equations and generalize a uniqueness criterion by Dulac concerning periodic solutions to equations of the formdot{x}=P(x,y), dot{y}=Q(x,y). In the second part we use this result to generalize a uniqueness theorem by de Figueiredo concerning periodic solutions to Liénard's equationddot{x} +f(x)dot{x} + g(x) = 0. By our method we are able to avoid the hitherto usual conditionxg(x) > 0, x {neq} 0, which excludes the possibility for the equation to have a dead band. Finally, we prove an existence theorem concerning periodic solutions to such equations. The use of the theorems is illustrated by a simple example in the last section.
    Original languageEnglish
    JournalIEEE Transactions on Circuits and Systems
    Volume27
    Issue number12
    Pages (from-to)1251-1254
    ISSN0098-4094
    DOIs
    Publication statusPublished - 1980

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