Existence and exponential stability for some stochastic neutral partial functional integrodifferential equations

Abstract

Abstract. The aim of this work is to study the existence, uniqueness and exponential stability of mild solutions for some stochastic neutral partial functional integrodifferential equations. We suppose that the linear part has a resolvent operator in the sense given in Grimmer [Transactions of the American Mathematical Society 273 (1982), 333–349]. The nonlinear part is assumed to be continuous and lipschitzian with respect to the second argument. Firstly, we study the existence of mild solutions. Secondly we give some results on the exponential stability in mean square sense. An example is provided to illustrate the results of this work.