Continuous selections of set of mild solutions of evolution inclusions

Electronic Journal of Differential Equations

关键词: Mild solutions;    differential inclusions;    integrodifferential inclusions.;   

DOI  :  

来源: DOAJ

【 摘 要 】

We prove the existence of continuous selections of the set valued map $xio mathcal{S}(xi)$ where $mathcal{S}(xi)$ is the set of all mild solutions of the evolution inclusions of the form $$displaylines{ dot{x}(t) in A(t)x(t)+int_0^tK(t,s)F(s,x(s))ds cr x(0)=xi ,quad tin I=[0,T], }$$ 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 $Iimes I$ with $tgeq s$ for all $t,sin I$ and $xi in X$.

【 授权许可】

Unknown