In this note we obtain the existence of local mild solutions for the following Cauchy problem governed by a semilinear evolution differential inclusion $x' \in A(t)x + F(t,x)$ $x(0) = x_0 \in E$, where ${A(t)}_{t\in [0,d]}$ is a family of linear operators in a Banach space E generating an evolution operator and F is a multifunction. We prove three existence theorems that improve or extend (in a broad sense) analogous results proved in this area.
Local mild solutions for semilinear evolution differential inclusions with lower semicontinuous type multifunctions
CARDINALI, Tiziana
2007
Abstract
In this note we obtain the existence of local mild solutions for the following Cauchy problem governed by a semilinear evolution differential inclusion $x' \in A(t)x + F(t,x)$ $x(0) = x_0 \in E$, where ${A(t)}_{t\in [0,d]}$ is a family of linear operators in a Banach space E generating an evolution operator and F is a multifunction. We prove three existence theorems that improve or extend (in a broad sense) analogous results proved in this area.File in questo prodotto:
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