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Existence of mild solutions for abstract semilinear evolution equations in Banach spaces. (English) Zbl 1235.34174

Summary: The nonlocal initial value problem,

x ' (t)=Ax(t)+f(t,x(t)),tI=[0,1],x(0)=g(x),

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×XX, g:C([0,1];X)X are given X-valued functions.

34G20Nonlinear ODE in abstract spaces
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
47N20Applications of operator theory to differential and integral equations
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