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Zbl 1179.34063
Liu, Qing; Yuan, Rong
Existence of mild solutions for semilinear evolution equations with non-local initial conditions.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 9, A, 4177-4184 (2009). ISSN 0362-546X

The authors study the existence of mild solutions for a class of semilinear evolution equations with nonlocal initial conditions. They mainly suppose that the nonlocal term $g$ is continuous or depends only on the value of $u$ in the interval $[\epsilon, T]$, where $\epsilon$ is small enough.
[Zhenbin Fan (Jiangsu)]
MSC 2000:
*34G20 Nonlinear ODE in abstract spaces
47D06 One-parameter semigroups and linear evolution equations
34A12 Initial value problems for ODE

Keywords: nonlocal initial condition; mild solutions; semilinear evolution equation; compact semigroup

Cited in: Zbl 1254.34079

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