FINDING PERIODIC-SOLUTIONS OF ORDINARY DIFFERENTIAL-EQUATIONS VIA HOMOTOPY METHOD

This paper deals with the problem of finding periodic solutions of ord inary differential equations. In our approach, by means of the homotop y method, the equation considered is linked to a simpler equation by i ntroducing a parameter. As a result, the problem of finding periodic s olutions is transformed into that of finding suitable solutions of the Cauchy problem; following the path of solutions of the Cauchy problem s starting from the Cauchy problem of a simpler equation, one can obta in the desired periodic solutions. In general, the solutions of the Ca uchy problem of the simpler equation are easily determined, relative t o periodic solutions of the equation considered. Consequently, an effi cient and global method of finding periodic solutions is established.