Estimation of unknown function of a class of retarded iterated integral inequalities

DOI

10.2991/isrme-15.2015.72How to use a DOI?

Keywords

integral inequality; unknown function; anlysis techniques; estimation

Abstract

It is well known that differential equations and integral equations are important tools to discuss the rule of natural phenomena. Various generalizations of the Gronwall-Bellman inequality are important tools in the study of existence, uniqueness, boundedness, stability, continuous dependence on the initial value and parameters, and other qualitative properties of solutions of differential equations and integral equation. In this paper, we discuss a class of retarded iterated integral inequalities, which includes a nonconstant term outside the integrals. By adopting novel analysis techniques, the upper bound of the embedded unknown function is estimated explicitly. The derived result can be applied in the study of solutions of ordinary differential equations and integral equations.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Jiting Huang
AU  - Wusheng Wang
AU  - Yun Ouyang
AU  - Yongzhou Qin
PY  - 2015/04
DA  - 2015/04
TI  - Estimation of unknown function of a class of retarded iterated integral inequalities
BT  - Proceedings of the 2015 International Conference on Intelligent Systems Research and Mechatronics Engineering
PB  - Atlantis Press
SP  - 337
EP  - 342
SN  - 1951-6851
UR  - https://doi.org/10.2991/isrme-15.2015.72
DO  - 10.2991/isrme-15.2015.72
ID  - Huang2015/04
ER  -