Differential Equations with a Small Parameter Attached to the Highest Derivatives and Some Problems in the Theory of Oscillations
- 1 December 1960
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IRE Transactions on Circuit Theory
- Vol. 7 (4) , 527-535
- https://doi.org/10.1109/TCT.1960.1086695
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\epsilonis 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
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