PERIODIC SOLUTION TO NONDENSELY DEFINED DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

Abstract

In this paper, we investigate the existence and uniqueness of periodic solution to a class of nondensely defined differential equations with infinite delay of the form
(
)
φ

 = + + ≥

 0 = ∈
( ) ( ) ( , ) , 0
t
du A B t u t g t u t dt u
where A: (A) ⊂ X → X is a nondensely defined linear operator on a Banach space X which satisfies the Hille - Yosida condition, (B(t))t≥0 is a family of bounded linear operator, g is ϕ - Lipschitz function and is appropriately phase space.
Keywords: Hille - Yosida condition, Periodic, Nondensely defined, Evolutionary process, Banach function space.