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.
- Green's function
- Linear and nonlinear ordinary differential equations
ASJC Scopus subject areas
- Applied Mathematics