Differential equations with bounded positive Green’s functions and generalized Aizerman’s hypothesis

被引：0

作者：

M. I. Gil’

机构：

[1] Ben Gurion University of the Negev,Department of Mathematics

来源：

Nonlinear Differential Equations and Applications NoDEA | 2004年 / 11卷

关键词：

34D20; 34D23; 34C10; 34D99; Linear and nonlinear ordinary differential equations ; Green’s function; positivity; stability;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We derive conditions for the positivity and boundedness of the Green functions of the higher order linear nonautonomous ODE. By virtue of these conditions, the existence of positive solutions for a class of nonlinear equations is proved. In addition, upper and lower estimates for the Green functions are established. Moreover, it is shown that nonlinear equations, having separated nonautonomous linear parts, satisfy the generalized Aizerman hypothesis on absolute stability, if they have the positive Green functions.

引用

页码：137 / 150

页数：13

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