Abstract
AbstractIn this paper we prove the existence of mild solutions for a problem governed by a semilinear non-autonomous second order differential inclusion where a stabilization of the solution is expected due to the control of the reaction term. In order to obtain our existence theorem, first we study a more general problem with a differential inclusion which involves a perturbation guided by an operator $$N :I \rightarrow C(C(I;X);X)$$
N
:
I
→
C
(
C
(
I
;
X
)
;
X
)
, where X is a Banach space. Finally we show an illustrative example of application of our results to a problem involving a wave equation.
Funder
Università degli Studi di Perugia
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
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