Abstract
The theory of differential inequalities plays a central role in the qualitative and quantitative study of differential equations. In this paper, we present several comparison results for a class of functional differential equations of first order with periodic boundary value conditions. The inequalities obtained are, generally speaking, of the following type: Pv ≤ 0 implies that v ≤ 0, where P is a functional differential operator subject to some boundary conditions, and v is an element of a prescribed space of functions. We first obtain several new results for the linear problem. Then, we consider a nonlinear differential equation as a functional perturbation of the original differential equation and give different comparison results. Our results improve and generalize previous estimates described in the literature.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.