MASSERA-TYPE THEOREM TO A CLASS  OF SEMI-LINEAR DIFFERENTIAL EQUATIONS

Nguyen Thi Loan; Dang Van Tien

Nguyen Thi Loan Faculty of Fundamental Sciences, PHENIKAA University
Dang Van Tien Department of Science Basic, Hung Yen University of Technology and Education

Keywords: Massera-type theorem, partial functional differential equations, periodic solutions

Abstract

In the present work, by applying a Massera-type theorem, we derive sufficient conditions for the existence and uniqueness of periodic solutions to a class of partial functional differential equations of the form

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here the operator A(t): E ⊇ D(A) → E is τ-periodic and possibly unbounded; the operator Γ(·, x(·)) takes values in a Banach space E, the function α takes values in the Banach space D(A), and are τ-periodic.

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