Comparison Principle And Stability Analysis For Several Kinds Of Stochastic Partial Functional Differential Equations

This thesis investigates the stability problem for several kinds of stochastic partial functional differential equations.By employing functional differential inequality technique,impulsive functional differential inequality technique and stochastic analysis theory,comparison principle for several kinds of stochastic partial functional differential equations are firstly established.Then,the comparison principle is applied to obtain several novel stability criteria of such equations.The main contributions of the thesis are summarized as follows.In Chapter 2,the pth moment stability,stability in probability and asymptotic stability for stochastic parabolic partial functional differential equations are investigated.Firstly,a comparison principle for stochastic parabolic partial functional differential equations is established.Secondly,various criteria for stability are obtained on the based of the comparison principle.Finally,two example are provided to illustrated the significance of the theoretical results.In Chapter 3,the mean square stability problem for a class of stochastic parabolic equa-tions with delay and Markovian switching is investigated.By establishing the comparison principle,the mean square stability,mean square uniform stability,mean square asymptotic stability and mean square exponential stability for the equations are obtained by using delay differential inequality and stochastic analysis techniques.Finally,an example is given to illus-trate the main theoretical result.In Chapter 4,the mean square stability problem for impulsive stochastic delayed reaction-diffusion Cohen-Grossberg neural networks is investigated.By employing stochastic analysis theory and impulsive functional differential inequality,comparison principle for a class of impulsive stochastic partial functional differential equations is established.By using the comparison principle,some sufficient conditions of impulsive stochastic delayed reaction-diffusion Cohen-Grossberg neural networks are derived by the stability of impulsive delay differential equation.An example is provided to show the effectiveness of the obtained results.In Chapter 5,the mean square stability problem for a class of impulsive stochastic delayed reaction-diffusion equations is investigated.By employing stochastic analysis theory,impulsive differential inequality technique and Razumikhin method,comparison principle for a class of impulsive stochastic delayed reaction-diffusion equations is firstly established.Then,by using the comparison principle,some sufficient conditions are derived to ensure the the mean square stability,mean square uniform stability,mean square asymptotic stability and mean square exponential stability of such equations.Finally,an example is provided to show the effectiveness of the proposed results.In Chapter 6,the mean square stability problem for a class of impulsive stochastic partial functional differential equations with Markovian switching is investigated.By employing impulsive functional differential inequality technique and stochastic analysis theory,comparison principle for a class of impulsive stochastic partial functional differential equations with Markovian switching is firstly established.Then,the comparison principle is applied to obtain several novel stability criteria of such equation.Finally,an example is provided to show the effectiveness of the proposed results.