Inequalities and exponential stability and instability in finite delay Volterra integro-differential equations

2012 ◽  
Vol 61 (3) ◽  
pp. 321-330 ◽  
Author(s):  
Murat Adıvar ◽  
Youssef N. Raffoul
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Finite Delay ◽  
Stability And Instability

ON EXPONENTIAL STABILITY FOR STOCHASTIC DELAY PARTIAL DIFFERENTIAL EQUATIONS

2009 ◽  
Vol 09 (01) ◽  
pp. 121-134
Author(s):  
GUOSHENG YU ◽  
BING LIU
Keyword(s):  
Partial Differential Equations ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Exponential Stability ◽  
Hilbert Spaces ◽  
Stability Criteria ◽  
Partial Differential ◽  
Stochastic Delay ◽  
Finite Delay ◽  
Delay Partial Differential Equations

This paper is concerned with the exponential stability of energy solutions to a nonlinear stochastic delay partial differential equations with finite delay in separable Hilbert spaces. Some exponential stability criteria are obtained by constructing the Lyapunov function. As an application, one example is also given to illustrate our results.

scholarly journals Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 988
Author(s):  
Pengju Duan
Keyword(s):  
Brownian Motion ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Mild Solution ◽  
Intermittent Control

The paper is devoted to studying the exponential stability of a mild solution of stochastic differential equations driven by G-Brownian motion with an aperiodically intermittent control. The aperiodically intermittent control is added into the drift coefficients, when intermittent intervals and coefficients satisfy suitable conditions; by use of the G-Lyapunov function, the p-th exponential stability is obtained. Finally, an example is given to illustrate the availability of the obtained results.

scholarly journals Existence and exponential stability in the pth moment for impulsive neutral stochastic integro-differential equations driven by mixed fractional Brownian motion

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xia Zhou ◽  
Dongpeng Zhou ◽  
Shouming Zhong
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Exponential Stability ◽  
Fractional Brownian Motion ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Fractional Power ◽  
Banach Fixed Point Theorem ◽  
Mixed Fractional Brownian Motion

Abstract This paper consider the existence, uniqueness and exponential stability in the pth moment of mild solution for impulsive neutral stochastic integro-differential equations driven simultaneously by fractional Brownian motion and by standard Brownian motion. Based on semigroup theory, the sufficient conditions to ensure the existence and uniqueness of mild solutions are obtained in terms of fractional power of operators and Banach fixed point theorem. Moreover, the pth moment exponential stability conditions of the equation are obtained by means of an impulsive integral inequality. Finally, an example is presented to illustrate the effectiveness of the obtained results.

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