Abstract
It is shown that all solutions of ẍ + 2x3 = p(t) are bounded, the notation indicating that p is periodic. It is not necessary to have a small parameter multiplying p.The essential step is to show by appeal to Moser's theorem that, under the mapping (of the initial-value plane) which corresponds to the equation, there are invariant simple closed curves. This implies also that there is an uncountable infinity of almost-periodic solutions and, for each positive integer m, an infinity of periodic solutions of least period 2mπ (2π being taken as the least period of p ).It is suggested that for a large class of equations the same attack would show all solutions of ẍ + g(x) = p(t) bounded. However, in order to show the method clearly, no generalisation is attempted here.
Sign-in/Register to access full text options 
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 callDisclaimer: 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.
