This paper deals with the semilinear multivalued evolution equationx'(t) + A(t)x(t) Є F(t, x(t)), t Є [a, b] and x Є E,in an arbitrary Banach space E.The linear operators {A(t) : t Є [a, b]} are densely defined on a common domain in E and generate a strongly continuous evolution system. We discuss the existence of mild periodic solutions, also in the case when the nonlinear term F depends on aretarded argument. We also show that in both cases the solutions set is compact. The proofs are based on topological arguments and make use of the theory of condensing multimaps.
Periodic Solutions of Semilinear Multivalued and Functional Evolution Equations in Banach Spaces / Cecchini, Simone; Malaguti, Luisa. - In: DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS. - ISSN 0971-3514. - STAMPA. - 17:(2009), pp. 365-377. [10.1007/s12591-009-0026-6]
Periodic Solutions of Semilinear Multivalued and Functional Evolution Equations in Banach Spaces
CECCHINI, Simone;MALAGUTI, Luisa
2009
Abstract
This paper deals with the semilinear multivalued evolution equationx'(t) + A(t)x(t) Є F(t, x(t)), t Є [a, b] and x Є E,in an arbitrary Banach space E.The linear operators {A(t) : t Є [a, b]} are densely defined on a common domain in E and generate a strongly continuous evolution system. We discuss the existence of mild periodic solutions, also in the case when the nonlinear term F depends on aretarded argument. We also show that in both cases the solutions set is compact. The proofs are based on topological arguments and make use of the theory of condensing multimaps.File | Dimensione | Formato | |
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