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Zbl 1241.34085
Shi, Hong-Bo; Li, Wan-Tong; Sun, Hong-Rui
Existence of mild solutions for abstract mixed type semilinear evolution equations. (English)
[J] Turk. J. Math. 35, No. 3, 457-472 (2011). ISSN 1300-0098; ISSN 1303-6149/e

The authors establish the existence of global mild solutions for an initial value problem associated with a first-order integrodifferential equation in a Banach space. In the case when the Banach space is ordered, the existence of positive mild solutions is obtained. The approach is based on a fixed point theorem due to {\it J. X. Sun} and {\it X. Y. Zhang} [Acta Math. Sin. 48, No. 3, 439--446 (2005; Zbl 1124.34342)].
[Sergiu Aizicovici (Athens/Ohio)]

MSC 2000:: *34K30 Functional-differential equations in abstract spaces
34G20 Nonlinear ODE in abstract spaces
47J35 Nonlinear evolution equations
47N20 Appl. of operator theory to differential and integral equations

Keywords: semilinear evolution equation; mild solution; fixed point theorem

Citations: Zbl 1124.34342

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