Journal of Sciences, Islamic Republic of Iran
PERIODIC SOLUTIONS OF CERTAIN THREE DIMENSIONAL AUTONOMOUS SYSTEMS
Abstract
There has been extensive work on the existence of periodic solutions for nonlinear
second order autonomous differantial equations, but little work regarding the third
order problems. The popular Poincare-Bendixon theorem applies well to the former
but not the latter (see [2] and [3]). We give a necessary condition for the existence of
periodic solutions for the third order autonomous systems, This may become useful
in further investigations. Our claims are proved and supported by certain examples.
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