( ?, c )-Periodic Mild Solutions to Non-Autonomous Abstract Differential Equations

Luciano Abadias, Edgardo Alvarez and Rogelio Grau
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Luciano Abadias: Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009 Zaragoza, Spain
Edgardo Alvarez: Departamento de Matemáticas y Estadística, Universidad del Norte, 080001 Barranquilla, Colombia
Rogelio Grau: Departamento de Matemáticas y Estadística, Universidad del Norte, 080001 Barranquilla, Colombia

Mathematics, 2021, vol. 9, issue 5, 1-15

Abstract: We investigate the semi-linear, non-autonomous, first-order abstract differential equation x ? ( t ) = A ( t ) x ( t ) + f ( t , x ( t ) , ? [ ? ( t , x ( t ) ) ] ) , t ? R . We obtain results on existence and uniqueness of ( ? , c ) -periodic (second-kind periodic) mild solutions, assuming that A ( t ) satisfies the so-called Acquistapace–Terreni conditions and the homogeneous associated problem has an integrable dichotomy. A new composition theorem and further regularity theorems are given.

Keywords: Acquistapace–Terreni conditions; non-autonomous semi-linear equation; periodic; ( ? , c )-periodic; delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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