Abstract
This paper investigates the existence of the extremal solutions to the integral boundary value problem for first-order impulsive functional integrodifferential equations with deviating arguments under the assumption of existing upper and lower solutions in the reversed order. The sufficient conditions for the existence of solutions were obtained by establishing several new comparison principles and using the monotone iterative technique. At last, a concrete example is presented and solved to illustrate the obtained results.
Highlights
Impulsive differential equations arise naturally from a wide variety of applications, such as control theory, physics, chemistry, population dynamics, biotechnology, industrial robotic, and optimal control 1–4
It is very important to develop a general theory for differential equations with impulses including some basic aspects of this theory
Let P C J, R {u : J → R | u t is continuous at t / tk, left continuous at t is continuously tk and u tk differentiable exists, k at t / tk, u
Summary
Impulsive differential equations arise naturally from a wide variety of applications, such as control theory, physics, chemistry, population dynamics, biotechnology, industrial robotic, and optimal control 1–4. We consider the following integral boundary value problem for firstorder impulsive functional integrodifferential equations with deviating arguments:. In 2009, Wang et al 27 successfully investigated boundary value problem for functional differential equations without impulses under the assumption of existing upper and lower solutions in the reversed order. As far as I am concerned, no paper has considered firstorder impulsive functional integrodifferential equations with integral boundary conditions and deviating arguments i.e., problem 1.1 under the assumption of existing upper and lower solutions in the reverse order. This paper fills this gap in the literature.
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 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.
