EXISTENCE OF THE PERIODIC SOLUTIONS OF A CLASS OF PERIODICITY PROBLEMS OF DIFFERENTIAL EQUATIONS AND RELATED ALGORITHMS
As is well known, the periodicity problem plays a central role in the qualitative theory of differential equations for its significance in the physical sciences. Hence, finding periodic solutions of ordinary differential equations is naturally an attracting topic. This paper mainly deals with the periodicity problem with the equality constraints as well as the inequality constraints. Under suitable conditions, we prove there exists a smooth path connecting a given point to the solution point. Numerical tracking of this path can lead to an implementable globally convergent algorithm for the periodicity problem.
periodicity problem, ordinary differential equations, smooth path.