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Periodic solutions of fractional degenerate differential equations with delay in Banach spaces

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Abstract

We characterize the Lp-well-posedness (resp. \(B_{p,q}^s\)-well-posedness) for the fractional degenerate differential equations with finite delay:

$$D^\alpha(Mu)(t)=Au(t)+Gu'_t+Fu_t+f(t),\;\;\;(t\in[0,2\pi]),$$

where α > 0 is fixed and A, M are closed linear operators in a Banach space X satisfying D(A) ∩ D(M) ≠ {0}, F and G are bounded linear operators from Lp([-2π,0];X) (resp. \(B_{p,q}^s\)([-2π,0];X)) into X. We also give a new example to which our abstract results may be applied.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Shangquan Bu

  2. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Gang Cai

Authors
  1. Shangquan Bu
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  2. Gang Cai
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Corresponding author

Correspondence to Gang Cai.

Additional information

This work was supported by the NSF of China (Grant No. 11571194, 11731010,11771063), the Natural Science Foundation of Chongqing(cstc2017jcyjAX0006), Science and Technology Project of Chongqing Education Committee (Grant No. KJ1703041, KJZDM201800501), 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. Periodic solutions of fractional degenerate differential equations with delay in Banach spaces. Isr. J. Math. 232, 695–717 (2019). https://doi.org/10.1007/s11856-019-1884-4

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  • DOI: https://doi.org/10.1007/s11856-019-1884-4

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