# Partially equi-integral $\phi_0$-stability of nonlinear differential systems

Volume 16, Issue 4, pp 472-480 Publication Date: December 15, 2016       Article History
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### Authors

Junyan Bao - College of Mathematics and Information Science, Hebei University, Baoding, 071002, China. Xiaojing Liu - College of Mathematics and Information Science, Hebei University, Baoding, 071002, China. Peiguang Wang - College of Electronic and Information Engineering, Hebei University, Baoding, 071002, China.

### Abstract

This paper introduces the notions of partially equi-integral stability and partially equi-integral $\phi_0$-stability for two differential systems, and establishes some criteria on stability relative to the $x$-component by using the cone-valued Lyapunov functions and the comparison technique. An example is also given to illustrate our main results.

### Keywords

• Differential systems
• partially integral stability
• partially integral $\phi_0$-stability
• cone-valued Lyapunov functions
• comparison technique.

•  34D20

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