Finding periodic solutions of ordinary differential equations via homotopy method

摘要

This paper deals with the problem of finding periodic solutions of ordinary differential equations. In our approach, by means of the homotopy method, the equation considered is linked to a simplier equation by introducing a parameter. As a result, the problem of finding periodic solutions is transformed into that of finding suitable solutions of the Cauchy problem. Following the path of solutions of the Cauchy problems starting from the Cauchy problem of a simpler equation, one can obtain the desired periodic solutions. In general, the solutions of the Cauchy problem of the simpler equation are easily determined, relative to periodic solutions of the equation considered. Consequently, an efficient and global method of finding periodic solutions is established.