Abstract

In this paper, we study the existence of periodic solutions for autonomous nonlinear ordinary differential equations of order n. Our method is based on the evaluation of Brouwer’s degree theory and making use of the homotopy invariance property of the topological degree and also suitable norm inequalities. For this, we prove two lemmas about the second and third order ODE systems and then present two theorems about the sufficient conditions for the existence of periodic solutions for the even and odd n‐order ODE respectively.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.