Electron. J. Diff. Equ.,
Vol. 2012 (2012), No. 110, pp. 115.
Existence of solutions for nonautonomous functional
evolution equations with nonlocal conditions
Xianlong Fu
Abstract:
In this work, we study the existence of mild solutions and strict
solutions of semilinear functional evolution equations with nonlocal
conditions, where the linear part is nonautonomous and generates a
linear evolution system. The fraction power theory and alphanorm
are used to discuss the problems so that the obtained results can be
applied to the equations in which the nonlinear terms involve
spatial derivatives. In particular, the compactness condition or
Lipschitz condition for the function g in the nonlocal conditions
appearing in various literatures is not required here. An example is
presented to show the applications of the obtained results
Submitted August 22, 2011. Published July 2, 2012.
Math Subject Classifications: 34K30, 34K05, 47D06, 47N20.
Key Words: Functional evolution equation; nonlocal condition;
linear evolution system; fractional power operator.
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Xianlong Fu
Department of Mathematics
East China Normal University
Shanghai, 200241 China
email: xlfu@math.ecnu.edu.cn

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