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Results in Mathematics

, 74:55 | Cite as

Hölder Continuous Solutions of Second Order Degenerate Differential Equations with Finite Delay

  • Shangquan Bu
  • Gang CaiEmail author
Article

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 AM 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.

Keywords

Well-posedness degenerate differential equations \({\dot{C}}^\alpha \)-multiplier Hölder continuous function spaces 

Mathematics Subject Classification

34G10 47D06 47A10 34K30 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  2. 2.School of Mathematical SciencesChongqing Normal UniversityChongqingChina

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