一类具有脉冲的二阶随机发展方程温和解的存在性

Existence of Mild Solutions for a Class of Second-order Stochastic Evolution Equations with Impulses

在Hilbert空间中研究一类具有瞬时脉冲的二阶非自治随机发展方程温和解的存在性。在不要求发展系统紧性的条件下,利用Sadovskii′s不动点定理和非紧性测度理论得到了该方程温和解的存在性结论,并给出一个例子说明了所获的结果。

The existence of mild solutions for a class of second-order non-autonomous stochastic evolution equations with instantaneous impulses is studied in Hilbert space.By using Sadovskii′s fixed point theorem and the theory of measure of noncompactness,the existence of the mild solution of the equation is obtained without the necessity of assuming that the corresponding evolution family is noncompact.Finally,one example is given to illustrate our main results.