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Nonlinear Retarded Integral Inequalities for Discontinuous Functions and its Applications

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Computer, Informatics, Cybernetics and Applications

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 107))

Abstract

It is well-known that integral inequality for continuous function is an important tool for studying the existence, uniqueness, boundedness, stability and other qualitative properties of solutions of differential equations and integral equations. The integral inequality for discontinuous function is an important tool for studying impulsive differential equations as well. To study the estimations of solution of nonlinear retarded impulsive integral equation, firstly retarded integral inequalities including the nonlinear composite function of discontinuous function are established, next the estimations of the unknown function of the integral inequalities are given by the methods of replacement, enlargement, differential, integral, segmentation, mathematical induction. Finally, the estimations obtained here are used to give the estimation of the solution of a class of nonlinear impulsive differential equation.

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Acknowledgments

This work is supported by the Natural Science Foundation of Guangxi Autonomous Region (0991265) and the Key Project of Hechi University (2009YAZ-N001)

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Authors and Affiliations

  1. Department of Mathematics, Hechi University, Yizhou, 546300, Guangxi, People’s Republic of China

    Wu-Sheng Wang & Anmin Tang

  2. School of Mathematics and Computer Science, Guilin University of Electronic Technology, Guilin, 541004, Guangxi, People’s Republic of China

    Zizun Li

Authors
  1. Wu-Sheng Wang
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  2. Zizun Li
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  3. Anmin Tang
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Corresponding author

Correspondence to Wu-Sheng Wang .

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Editors and Affiliations

  1. Chinese Academy of Engineering, Beijing, China, People's Republic

    Xingui He

  2. Zhejiang Gongshang University, Beijing, China, People's Republic

    Ertian Hua

  3. Zhejiang Gongshang University, Hangzhou, China, People's Republic

    Yun Lin

  4. , School of Automation, Wuhan University of Technology, East District of Wuhan University, Luoshi Road 122, Wuhan, 4300, China, People's Republic

    Xiaozhu Liu

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Wang, WS., Li, Z., Tang, A. (2012). Nonlinear Retarded Integral Inequalities for Discontinuous Functions and its Applications. In: He, X., Hua, E., Lin, Y., Liu, X. (eds) Computer, Informatics, Cybernetics and Applications. Lecture Notes in Electrical Engineering, vol 107. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1839-5_17

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  • DOI: https://doi.org/10.1007/978-94-007-1839-5_17

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-1838-8

  • Online ISBN: 978-94-007-1839-5

  • eBook Packages: EngineeringEngineering (R0)

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