Abstract
In this paper, we give necessary and sufficient conditions for the \(L^p\)-well-posedness (resp. \(B_{p,q}^s\)-well-posedness) for the third order degenerate differential equation with finite delay: \((Mu)'''(t) + (Nu)''(t)= Au(t) + Bu'(t) + Gu''_t + Fu'_t + Hu_t + f(t)\) on \([0,2\pi ])\) with periodic boundary conditions \((Mu)(0) = (Mu)(2\pi )\), \((Mu)'(0) = (Mu)'(2\pi )\), \((Mu)''(0) = (Mu)''(2\pi )\), where A, B, M and N are closed linear operators on a Banach space X satisfying \(D(A)\cap D(B)\subset D(M)\cap D(N)\), the operators G, F and H are bounded linear from \(L^p([-2\pi ,0];X)\) (resp. \(B_{p,q}^s([-2\pi ,0];X)\)) into X.
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Acknowledgements
The authors are grateful to the anonymous referee for useful remarks and to call our attention to Theorem 1.1 in [9] allowing us to simplify considerably the proofs of Proposition 2.2 and Proposition 3.1.
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This work was supported by the NSF of China (Grant Nos. 11731010, 11771063, 11971082), the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0455), Science and Technology Project of Chongqing Education Committee (Grant No. KJZD-K201900504) and the Program of Chongqing Innovation Research Group Project in University (Grant No. CXQT19018).
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Bu, S., Cai, G. Well-Posedness of Third Order Degenerate Differential Equations with Finite Delay in Banach Spaces. Results Math 76, 85 (2021). https://doi.org/10.1007/s00025-021-01376-8
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DOI: https://doi.org/10.1007/s00025-021-01376-8