主题：Hartman--Wintner and Bihari--type theorems for Differential Equations
主讲人：John Andrew Appleby
时间：2017年5月24日(周三)， 下午15:00 ~ 16:30
John Andrew Appleby，都柏林城市大学数学科学系教授, 博士生导师， 出版专著4部，发表论文60余篇。研究领域：随机微分方程。
Theorems of Hartman--Wintner type in the theory of differential equations typically consider perturbed linear equations, and determine conditions under which the solution of the perturbed equation is asymptotic to the solution of the unperturbed equation. In this talk, we concentrate on equations with growing solutions. First, we give conditions under which Hartman--Wintner results can be extended to sublinear ordinary differential equations. Second, for superlinear differential equations, Hartman--Wintner results are unsuitable, so we establish results which may be thought of as extensions of Bihari's inequality. In both cases, we demonstrate that our conditions are sharp, or even necessary and sufficient. The results are applied to determine the exact asymptotic behaviour of sublinear and superlinear stochastic differential equations, including a process we call subexponential Brownian motion.