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Global existence for semilinear evolution equations with nonlocal conditions. (English) Zbl 0884.34069
The authors apply Schauder’s fixed-point theory to differential equations in Banach spaces, $x'(t)= Ax(t)+ f(t,x(t))$ with nonlocal initial conditions of the type $x(0)+ g(x)= x_0.$ Here, $$t\in[0, b]$$, and some general assumptions on $$g: C([0,b], X)\to X$$ and $$f:[0, b]\times X\to X$$ are given which guarantee the existence of a solution $$x\in C([0,b], X)$$.

MSC:
 34G20 Nonlinear differential equations in abstract spaces 34K30 Functional-differential equations in abstract spaces
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