一类中立型随机偏微分方程概周期解的存在性和唯一性

Existence and Uniqueness of Almost Periodic Solutions to Some Neutral Stochastic Differential Equations

最近,P.Bezandry和T.Diagana(P.Bezandry,T.Diagana.Appl.Anal.,2007,117:1-10.)引入了均值概周期的概念,研究了一类随机时滞演化方程,并获得了其均值概周期存在和唯一的充分条件.我们将应用不动点理论和分数幂算子方法,获得一类中立型随机偏微分方程在均方意义下的概周期解的存在性和唯一性的充分条件.

P. Bezandry and T. Diagana introduced a new concept of square-mean almost periodicity. They established the existence and uniqueness of square-mean almost periodic mild solutions to some stochastic differential equations and some functional integrodifferential stochastic evolution equations. Sufficient conditions for the existence and uniqueness of a square-mean almost periodic mild solution of a class of abstract neutral stochastic differential equations in a real separable Hilbert space are derived with the help of the Banach fixed point theorem and the fractional power of operators.