Abstract
In this paper, we characterize the \(C^\alpha \)-well-posedness of the second order degenerate differential equation with finite delay \((Mu)''(t) = Au(t) + Fu_t + f(t)\), (\(t\in {\mathbb R}\)) by using known operator-valued Fourier multiplier results on \(C^\alpha ({\mathbb R}; X)\), where A, M are closed linear operators on a complex Banach space X satisfying \(D(A)\cap D(M) \not =\{0\}\), \(r > 0\) is fixed and F is a bounded linear operator from \(C([-r, 0]; X)\) into X.
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This work is supported by the NSF of China (11731010, 11771063, 11571194), the Natural Science Foundation of Chongqing(cstc2017jcyjAX0006, KJZDM201800501), Science and Technology Project of Chongqing Education Committee (Grant No. KJ1703041), the University Young Core Teacher Foundation of Chongqing (020603011714), Talent Project of Chongqing Normal University (Grant No. 02030307-00024).
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Bu, S., Cai, G. Hölder Continuous Solutions of Second Order Degenerate Differential Equations with Finite Delay. Results Math 74, 55 (2019). https://doi.org/10.1007/s00025-019-0982-2
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DOI: https://doi.org/10.1007/s00025-019-0982-2