MASSERA -TYPE THEOREM FOR DIFFERENTIAL EQUATIONS IN THE SPACE OF BOUNDED CONTINUOUS FUNCTIONS

Tóm tắt

Consider the class of the differential equations in the form

t (x t h t B t x t k t t ( ) + = +  ( )) ( ) ( ) ( ), + . (1)

By using Massera-type theorem, we demonstrate the existence and uniqueness of periodic solutions for the equation (1), with the operator B t X D B X ( ) : ( )  → is  - periodic and possibly unbounded on a Banach space X; the function h gets the value in the Banach space D(B), the function k attains the value in the Banach space X and is  -periodic.