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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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    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. 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.

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