Almost sure exponential stability for stochastic neutral partial functional differential equations

Stochastics ◽  
2005 ◽  
Vol 77 (2) ◽  
pp. 139-154 ◽  
Author(s):  
T. E. Govindan
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Almost Sure Exponential Stability ◽  
Partial Functional Differential Equations ◽  
Functional Differential

scholarly journals Exponential Stability in Mean Square for Neutral Stochastic Partial Functional Differential Equations with Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Nan Ding
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Mild Solution ◽  
Semigroup Theory ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Mean Square ◽  
Partial Functional Differential Equations ◽  
Functional Differential ◽  
Stability In Mean Square

We discuss the exponential stability in mean square of mild solution for neutral stochastic partial functional differential equations with impulses. By applying impulsive Gronwall-Bellman inequality, the stochastic analytic techniques, the fractional power of operator, and semigroup theory, we obtain some completely new sufficient conditions ensuring the exponential stability in mean square of mild solution for neutral stochastic partial functional differential equations with impulses. Finally, an example is provided to illustrate the obtained theory.

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