Abstract
Some precise descriptions of the structure and behavior of bounded solutions for a class of nonautonomous second-order differential equations are obtained. The nonautonomous differential equations here are in the form x ″ = f ( θ t h , x , x ′ ) , where the driving system θ is defined in a compact base space H and the vector field f ( h , x , p ) is strictly increasing in state variable x on some interval ( a , b ) . The stability of the structure of bounded solutions with respect to parameter perturbations in f is also addressed.
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