مرکز منطقه ای اطلاع رساني علوم و فناوري - Differential Equations with a Small Parameter Attached to the Highest Derivatives and Some Problems in the Theory of Oscillations

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 :

Issue :

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.