Stability of higher-order nonlinear impulsive differential equations
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Authors
Shuhong Tang
- School of Information and Control Engineering, Weifang University, Weifang, Shandong 261061, P. R. China.
Akbar Zada
- Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan.
Shah Faisal
- Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan.
M. M. A. El-Sheikh
- Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Koom 32511, Egypt.
Tongxing Li
- LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, Shandong 276005, P. R. China.
- School of Informatics, Linyi University, Linyi, Shandong 276005, P. R. China.
Abstract
For a higher-order nonlinear impulsive ordinary differential equation, we present the concepts of Hyers-
Ulam stability, generalized Hyers-Ulam stability, Hyers-Ulam{Rassias stability, and generalized Hyers-
Ulam-Rassias stability. Furthermore, we prove the generalized Hyers-Ulam-Rassias stability by using integral
inequality of Grönwall type for piecewise continuous functions. These results extend related contributions
to the corresponding first-order impulsive ordinary differential equation. Hyers-Ulam stability,
generalized Hyers-Ulam stability, and Hyers-Ulam-Rassias stability can be discussed by the same methods.
Share and Cite
ISRP Style
Shuhong Tang, Akbar Zada, Shah Faisal, M. M. A. El-Sheikh, Tongxing Li, Stability of higher-order nonlinear impulsive differential equations, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4713--4721
AMA Style
Tang Shuhong, Zada Akbar, Faisal Shah, El-Sheikh M. M. A., Li Tongxing, Stability of higher-order nonlinear impulsive differential equations. J. Nonlinear Sci. Appl. (2016); 9(6):4713--4721
Chicago/Turabian Style
Tang, Shuhong, Zada, Akbar, Faisal, Shah, El-Sheikh, M. M. A., Li, Tongxing. "Stability of higher-order nonlinear impulsive differential equations." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4713--4721
Keywords
- Hyers-Ulam stability
- generalized Hyers-Ulam stability
- Hyers-Ulam-Rassias stability
- generalized Hyers-Ulam-Rassias stability
- nonlinear impulsive differential equation
- higher-order
- Grönwall inequality.
MSC
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