Geodesic
Continuous selections of set of mild solutions of evolution inclusions
Electronic journal of differential equations, Tome 2005 (2005)
Zbl   EuDML
We prove the existence of continuous selections of the set valued map

$\displaylines{ \dot{x}(t) \in A(t)x(t)+\int_0^tK(t,s)F(s,x(s))ds \cr x(0)=\xi ,\quad t\in I=[0,T], }$

where $F$ is a lower semi continuous set valued map Lipchitzean with respect to $x$ in a separable Banach space $X, A$ is the infinitesimal generator of a $C_0$-semi group of bounded linear operators from $X$ to $X$, and $K(t,s)$ is a continuous real valued function defined on $I\times I$ with $t\geq s$ for all $t,s\in I$ and $\xi \in X$.
Classification : 34A60, 34G20
Keywords: mild solutions, differential inclusions, integrodifferential inclusions 
Anguraj,  Annamalai; Murugesan,  Chinnagounder. Continuous selections of set of mild solutions of evolution inclusions. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a230/
@article{EJDE_2005__2005__a230,
     author = {Anguraj,  Annamalai and Murugesan,  Chinnagounder},
     title = {Continuous selections of set of mild solutions of evolution inclusions},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1075.34052},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a230/}
}
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