随机Leray-Schauder定理与随机Hammerstein方程

A RANDOMVERSION OF THE LERAY-SCHAUDER THEOREM AND RANDOM HAMMERSTEIN EQUATIONS

本文在可分Banach空间中证明随机Leray-Schauder定理,它是[10]的随机推广并改进[6]中相应的结果。作为其应用,讨论一类涉及紧单调算子的随机Hammerstein方程的解。本文还讨论了涉及非紧单调算子的随机Hammerstein方程和存在定理,它们是[2]的两个主要结果的随机推广。

In this note, we prove a random version of the Leray-Schauder theorem of [10] inseparable Banach spaces, and improve the corresponding result in [6]. As its application,we get an existence theorem for a class of random Hammerstein equations involving compactmonotone operators. We also discuss existence theorems for random Hammerstein equationsof noncompact monotone operators, which are stochastic generalizations of main results,theorem 1 and 3, in [2].