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Existence of Solutions for Kirchhoff-Type Fractional Dirichlet Problem with p -Laplacian

Author

Listed:
  • Danyang Kang

    (Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China)

  • Cuiling Liu

    (Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China)

  • Xingyong Zhang

    (Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
    School of Mathematics and Statistics, Central South University, Changsha 410083, China)

Abstract

In this paper, we investigate the existence of solutions for a class of p -Laplacian fractional order Kirchhoff-type system with Riemann–Liouville fractional derivatives and a parameter λ . By mountain pass theorem, we obtain that system has at least one non-trivial weak solution u λ under some local conditions for each given large parameter λ . We get a concrete lower bound of the parameter λ , and then obtain two estimates of weak solutions u λ . We also obtain that u λ → 0 if λ tends to ∞ . Finally, we present an example as an application of our results.

Suggested Citation

  • Danyang Kang & Cuiling Liu & Xingyong Zhang, 2020. "Existence of Solutions for Kirchhoff-Type Fractional Dirichlet Problem with p -Laplacian," Mathematics, MDPI, vol. 8(1), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:106-:d:306484
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    References listed on IDEAS

    as
    1. Zhao, Yulin & Chen, Haibo & Qin, Bin, 2015. "Multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 417-427.
    2. Junping Xie & Xingyong Zhang, 2018. "Infinitely Many Solutions for a Class of Fractional Impulsive Coupled Systems with -Laplacian," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-14, May.
    3. Lim, S.C., 2006. "Fractional derivative quantum fields at positive temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 269-281.
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