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Positive solutions for eigenvalue problems of fractional differential equation with generalized p-Laplacian

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  • Han, Zhenlai
  • Lu, Hongling
  • Zhang, Chao

Abstract

In this paper, we investigate the existence of positive solutions for the eigenvalue problem of nonlinear fractional differential equation with generalized p-Laplacian operatorD0+β(ϕ(D0+αu(t)))=λf(u(t)),00 is a parameter, and f:(0,+∞)→(0,+∞) is continuous. By using the properties of Green function and Guo–Krasnosel’skii fixed-point theorem on cones, several new existence results of at least one or two positive solutions in terms of different eigenvalue interval are obtained. Moreover, the nonexistence of positive solution in term of the parameter λ is also considered.

Suggested Citation

  • Han, Zhenlai & Lu, Hongling & Zhang, Chao, 2015. "Positive solutions for eigenvalue problems of fractional differential equation with generalized p-Laplacian," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 526-536.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:526-536
    DOI: 10.1016/j.amc.2015.01.013
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    References listed on IDEAS

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    1. Moustafa El-Shahed, 2007. "Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2007(1).
    2. Xinguang Zhang & Lishan Liu & Benchawan Wiwatanapataphee & Yonghong Wu, 2012. "Positive Solutions of Eigenvalue Problems for a Class of Fractional Differential Equations with Derivatives," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Li, Xiaoyan, 2021. "Comment for “Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel”," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. SunAe Pak & KumSong Jong & KyuNam O & HuiChol Choi, 2020. "Existence Results for a Class of p -Laplacian Fractional Differential Equations with Integral Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    3. Haoran Zhang & Zhaocai Hao & Martin Bohner, 2024. "Multiple and Nonexistence of Positive Solutions for a Class of Fractional Differential Equations with p -Laplacian Operator," Mathematics, MDPI, vol. 12(23), pages 1-14, December.
    4. Liu, Xiping & Jia, Mei, 2019. "Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 230-242.
    5. Ravi P. Agarwal & Ekaterina Madamlieva, 2025. "Analysis of Mild Extremal Solutions in Nonlinear Caputo-Type Fractional Delay Difference Equations," Mathematics, MDPI, vol. 13(8), pages 1-27, April.

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