Existence of solutions for nonlinear impulsive \(q_k\)-difference equations with first-order \(q_k\)-derivatives
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Authors
Changlong Yu
- College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China.
Jufang Wang
- College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China.
Yanping Guo
- College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China.
Abstract
In this paper, we study the nonlinear second-order impulsive \(q_k\)-difference equations with Sturm-Liouville
type, in which nonlinear team and impulsive teams are dependent on first-order \(q_k\)-derivatives. We obtain
the existence and uniqueness results of solutions for the problem by Banach's contraction mapping principle
and Schaefer's fixed point theorems. Finally, we give two examples to demonstrate the use of the main
results.
Share and Cite
ISRP Style
Changlong Yu, Jufang Wang, Yanping Guo, Existence of solutions for nonlinear impulsive \(q_k\)-difference equations with first-order \(q_k\)-derivatives, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2615--2630
AMA Style
Yu Changlong, Wang Jufang, Guo Yanping, Existence of solutions for nonlinear impulsive \(q_k\)-difference equations with first-order \(q_k\)-derivatives. J. Nonlinear Sci. Appl. (2016); 9(5):2615--2630
Chicago/Turabian Style
Yu, Changlong, Wang, Jufang, Guo, Yanping. "Existence of solutions for nonlinear impulsive \(q_k\)-difference equations with first-order \(q_k\)-derivatives." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2615--2630
Keywords
- boundary value problem
- \(q_k\)-derivative
- \(q_k\)-integral
- impulsive \(q_k\)-difference equation
- fixed point theorem.
MSC
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