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Zbl 1235.34174
Zhu, Tao; Song, Chao; Li, Gang
Existence of mild solutions for abstract semilinear evolution equations in Banach spaces. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 1, 177-181 (2012). ISSN 0362-546X

Summary: The nonlocal initial value problem, $$\cases x'(t)=Ax(t)+f(t,x(t)), \quad t\in I=[0,1],\\ x(0)=g(x),\endcases$$ where $A$ is the infinitesimal generator of a strongly continuous semigroup of bounded linear operators (i.e. $C_0$-semigroup) $T(t)$ in Banach space $X$, and $f:I\times X\to X$, $g:C([0,1];X)\to X$ are given $X$-valued functions.

MSC 2000:: *34G20 Nonlinear ODE in abstract spaces
34A12 Initial value problems for ODE
47N20 Appl. of operator theory to differential and integral equations

Keywords: measure of noncompactness; nonlocal conditions; semigroup; mild solution

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