Year-end Sale % OFF 
Abstract
For abstract linear nonautonomous boundary differential equations with an almost automorphic forcing term, a Massera type criterion is established for the existence of an almost automorphic solution with the help of the spectrum of monodromy operator, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations.
Highlights
A classical result of Massera in his landmark paper [1] says that a necessary and sufficient condition for an ω-periodic linear scalar ordinary differential equation to have an ω-periodic solution is that it has a bounded solution on the positive half line
There has been an increasing interest in the almost automorphy of dynamical systems, which is first introduced by Bochner [13] and is more general than the almost periodicity and attracts more and more attention
One can see [14, 15] for a complete background on almost automorphic functions and see the important Memoirs [16] for almost automorphic dynamics
Summary
A classical result of Massera in his landmark paper [1] says that a necessary and sufficient condition for an ω-periodic linear scalar ordinary differential equation to have an ω-periodic solution is that it has a bounded solution on the positive half line. We will make an attempt to give an extension of the classical result of Massera to almost automorphic solutions of nonautonomous boundary differential equations (or sometimes, nonautonomous boundary Cauchy problems), which are an abstract formulation of partial differential equations with boundary conditions modeling natural phenomena such as retarded differential (difference) equations, dynamic population equations, and boundary control problems, and has been widely studied (see [25] and references cited therein).
Sign-in/Register to view highlights & summary 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 callMore From: Electronic Journal of Qualitative Theory of Differential Equations
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.
