Abstract
The stability of the periodic solution of the system of equations dz dt = f (z,t) with discontinous periodic [ f( z, t + r) = f( z, t)] right-hand sides [ z and f are n-dimensional vector columns with coordinates z i and f i ( i = 1, ·, n)] has been investigated by Aizerman and Gantmakher [1]. Establishing what should be understood by the linear approximation in this “discontinuous” case, the authors have proved theorems analogous to those of Liapunov. The present paper deals with the stability of any solution (periodic or nonperiodic) of system (0.1) with discontinuous nonperiodic right-hand sides. For this, use is made of the condition for the discontinuities of the solution of the linear approximation introduced in paper [1] for periodic systems. Two criteria of stability are established which are generalizations of the corresponding theorems of Persidskii [2] and Perron [3], proved by these authors for continuous systems.
Published Version
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.
