• DocumentCode
    1202057
  • Title

    Differential Equations with a Small Parameter Attached to the Highest Derivatives and Some Problems in the Theory of Oscillations

  • Author

    Mishchenko, E.F. ; Pontryagin, L.S.

  • Volume
    7
  • Issue
    4
  • fYear
    1960
  • fDate
    12/1/1960 12:00:00 AM
  • Firstpage
    527
  • Lastpage
    535
  • Abstract
    This paper presents a brief review, for the most part, of the authors\´ results concerning systems of differential equations of the form \\epsilon dot{x}^1 = f^i(x^1,\\cdots ,x^k,y^1,\\cdots ,y^l) i =1, 2,\\cdots ,k dot{y}^i = g^i(x^1,\\cdots ,x^k,y^1,\\cdots ,y^l) j =1,2,\\cdots , where \\epsilon is a small positive parameter. The emphasis is on periodic solutions of such systems which are close to discontinuous solutions. Such periodic solutions are mathematical representations of relaxation oscillations which are encountered in various mechanical, electrical and radio systems.
  • Keywords
    Assembly; Capacitors; Differential equations; Electron tubes; Inductance; Inductors; Joining processes; Nonlinear equations; Stability; Wires;
  • fLanguage
    English
  • Journal_Title
    Circuit Theory, IRE Transactions on
  • Publisher
    ieee
  • ISSN
    0096-2007
  • Type

    jour

  • DOI
    10.1109/TCT.1960.1086695
  • Filename
    1086695
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1202057