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Zbl 0884.34069
Ntouyas, S.K.; Tsamatos, P.Ch.
Global existence for semilinear evolution equations with nonlocal conditions.
(English)
[J] J. Math. Anal. Appl. 210, No.2, 679-687 (1997). ISSN 0022-247X

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 $x\in C([0,b], X)$.
[R.Illner (Victoria)]
MSC 2000:
*34G20 Nonlinear ODE in abstract spaces
34K30 Functional-differential equations in abstract spaces

Keywords: differential equations in Banach spaces; initial conditions

Cited in: Zbl 1046.34080

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