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Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations

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  • Jing Wu
  • Xinguang Zhang

Abstract

We study the eigenvalue interval for the existence of positive solutions to a semipositone higher order fractional differential equation -𝒟tμx(t) = λf(t,x(t),𝒟tμ1x(t),𝒟tμ2x(t),… ,𝒟tμn-1x(t))…𝒟tμix(0) = 011001, ≤i≤n-,𝒟tμn-1+1x()=, 𝒟tμn-1x()=∑j=1m-2aj𝒟tμn-1x(ξj), where n − 1

Suggested Citation

  • Jing Wu & Xinguang Zhang, 2012. "Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:740760
    DOI: 10.1155/2012/740760
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    References listed on IDEAS

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    1. Min Jia & Xin Liu & Xuemai Gu, 2012. "Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional‐Order Integral Boundary Value Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. D. G. De Figueiredo & P. L. Lions & R. D. Nussbaum, 1982. "A Priori Estimates and Existence of Positive Solutions of Semilinear Elliptic Equations," Springer Books, in: David G. Costa (ed.), Djairo G. de Figueiredo - Selected Papers, edition 127, pages 133-155, Springer.
    3. Min Jia & Xin Liu & Xuemai Gu, 2012. "Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-21, October.
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    Cited by:

    1. Zhang, Xinguang & Liu, Lishan & Wu, Yonghong & Wiwatanapataphee, B., 2015. "The spectral analysis for a singular fractional differential equation with a signed measure," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 252-263.
    2. Hicham Ait Mohammed & Safa M. Mirgani & Brahim Tellab & Abdelkader Amara & Mohammed El-Hadi Mezabia & Khaled Zennir & Keltoum Bouhali, 2025. "Hyers–Ulam Stability Results of Solutions for a Multi-Point φ -Riemann-Liouville Fractional Boundary Value Problem," Mathematics, MDPI, vol. 13(9), pages 1-25, April.
    3. Wang, Ying & Liu, Lishan & Zhang, Xinguang & Wu, Yonghong, 2015. "Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 312-324.
    4. Weiwei Liu & Lishan Liu, 2021. "Existence of Positive Solutions for a Higher-Order Fractional Differential Equation with Multi-Term Lower-Order Derivatives," Mathematics, MDPI, vol. 9(23), pages 1-23, November.
    5. Wenquan Wu & Xiangbing Zhou, 2013. "Eigenvalue of Fractional Differential Equations with -Laplacian Operator," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-8, March.

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