Abstract
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 non-linear 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.
| Original language | English |
|---|---|
| Pages (from-to) | 137-150 |
| Number of pages | 14 |
| Journal | Nonlinear Differential Equations and Applications |
| Volume | 11 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Jan 2004 |
Keywords
- Green's function
- Linear and nonlinear ordinary differential equations
- Positivity
- Stability
ASJC Scopus subject areas
- Analysis
- Applied Mathematics