Periodic Solutions of Infinite Delay Evolution Equations
نویسندگان
چکیده
منابع مشابه
Bounded and periodic solutions of infinite delay evolution equations
For A(t) and f (t, x, y) T -periodic in t , we consider the following evolution equation with infinite delay in a general Banach space X: u′(t)+A(t)u(t)= f (t, u(t), ut ), t > 0, u(s)= φ(s), s 0, (0.1) where the resolvent of the unbounded operator A(t) is compact, and ut (s) = u(t + s), s 0. By utilizing a recent asymptotic fixed point theorem of Hale and Lunel (1993) for condensing operators t...
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We study finite delay evolution equation { x′(t) = Ax(t) + F (t, xt), t ≥ 0, x0 = φ ∈ C ([−r, 0] , E) , where linear operator A is non-densely defined and satisfies the Hille-Yosida condition. First we obtain some properties of “integral solutions” in this case, and prove the compactness of an operator determined by integral solutions. This allows us to apply Horn’s fixed point theorem to prove...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2000
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.6896