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The European Physical Journal Special Topics

, Volume 226, Issue 16–18, pp 3445–3456 | Cite as

Extremal points for fractional boundary value problems

  • Johnny Henderson
  • Charles NelmsJr.
  • Dingjiang Wang
  • Aijun Yang
Regular Article
  • 14 Downloads
Part of the following topical collections:
  1. Fractional Dynamical Systems - Recent Trends in Theory and Applications

Abstract

This article is concerned with characterizing the first extremal point, b0, for a Riemann–Liouville fractional boundary value problem, Dα0+y + p(t)y = 0, 0 < t < b, y(0) = y(0) = y(b) = 0, 2 < α ≤ 3, by applying the theory of u0-positive operators with respect to a suitable cone in a Banach space. The key argument is that a mapping, which maps a linear, compact operator, depending on b to its spectral radius, is continuous and strictly increasing as a function of b. Furthermore, an application to a nonlinear case is given.

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Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Johnny Henderson
    • 1
  • Charles NelmsJr.
    • 2
  • Dingjiang Wang
    • 3
  • Aijun Yang
    • 1
    • 3
  1. 1.Baylor University, Department of MathematicsWacoUSA
  2. 2.Wayland Baptist University, School of Math and SciencePlainviewUSA
  3. 3.Zhejiang University of Technology, College of ScienceHangzhouP.R. China

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