SOME BOUNDARY VALUE PROBLEMS FOR A NON-LINEAR THIRD ORDER O.D.E.

Abstract

Existence of periodic solutions for non-linear third order autonomous differential equation (O.D.E.) has not been investigated to as large an extent as non-linear second order. The popular Poincare-Bendixon theorem applicable to second order equation is not valid for third order equation (see [3]). This conclusion opens a way for further investigation.