Practical stability in relation to a part of variables of stochastic pantograph differential equations

Abstract

The main purpose of this paper is to investigate the practical stability in relation to a part of the variables of stochastic pantograph differential equations (SPDEs, in short). With the aid of Lyapunov function method, the criterions of the global practical uniform asymptotic stability and the global practical uniform p-th moment exponential stability in relation to a part of variables of SPDEs are established. An illustrative example is given to show the effectiveness and feasibility of the proposed results on the practical stability with respect to a part of variables.

Keywords:

• Stochastic pantograph differential equation
• practical stability
• asymptotic stability
• exponential stability

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [11871076].