Abstract
In this paper, we discuss a class of retarded nonlinear integral inequalities and give an upper bound estimation of an unknown function by the integral inequality technique. This estimation can be used as a tool in the study of differential-integral equations with the initial conditions.MSC:26D10, 26D15, 26D20, 34A12, 34A40.
Highlights
Gronwall-Bellman inequalities [, ] can be used as important tools in the study of existence, uniqueness, boundedness, stability, and other qualitative properties of solutions of differential equations, integral equations, and integral-differential equations
There can be found a lot of generalizations of Gronwall-Bellman inequalities in various cases from literature (e.g., [ – ])
Lemma (Abdeldaim and Yakout [ ]) We assume that u(t) and f (t) are nonnegative realvalued continuous functions defined on I = [, ∞) and they satisfy the inequality t
Summary
Gronwall-Bellman inequalities [ , ] can be used as important tools in the study of existence, uniqueness, boundedness, stability, and other qualitative properties of solutions of differential equations, integral equations, and integral-differential equations. Lemma (Abdeldaim and Yakout [ ]) We assume that u(t) and f (t) are nonnegative realvalued continuous functions defined on I = [ , ∞) and they satisfy the inequality t We discuss a class of retarded nonlinear integral inequalities and give an upper bound estimation of an unknown function by the integral inequality technique.
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.
