PERIODIC SOLUTION TO NONDENSELY DEFINED DIFFERENTIAL EQUATIONS WITH INFINITE DELAY
Nội dung chính của bài viết
Tóm tắt
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.