On the existence of mild solutions of semilinear evolution differential inclusions
By T. Cardinali, P. Rubbioni. 2005
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Abstract In this paper we deal with a Cauchy problem governed by the following semilinear evolution differential inclusion: x ′ ( t ) ∈ A ( t ) x ( t ) + F ( t , x ( t ) ) and with initial data x ( 0 ) = x 0 ∈ E , where { A ( t ) } t ∈ [ 0 , d ] is a family of linear operators in the Banach space E generating an evolution operator and F is a Caratheodory type multifunction. We prove the existence of local and global mild solutions of the problem. Moreover, we obtain the compactness of the set of all global mild solutions. In order to obtain these results, we define a generalized Cauchy operator. Our existence theorems respectively contain the analogous results provided by Kamenskii, Obukhovskii and Zecca [Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, De Gruyter Ser. Nonlinear Anal. Appl., vol. 7, de Gruyter, Berlin, 2001] for inclusions with constant operator.
Subfields: Applied Mathematics, Geometry and Topology, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/0246d4b1be2b2f1a09b490f74aad0c42c578d25d
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In Applied Mathematics
In Geometry and Topology
In Modeling and Simulation
Citations in the corpus
- Impulsive mild solutions for semilinear differential inclusions with nonlocal conditions in Banach spaces (2012, methodology): “This is clear by taking account of comments in Remark 4 of [18] and by observing that every impulsive mild solution of (INP) can be rewritten as an impulsive mild solution of a nonlocal Cauchy problemwhere the linear part of the differential inclusion is autonomous.”