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Nontrivial solutions for impulsive fractional differential equations via Morse theory

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  • Zhao, Yulin
  • Chen, Haibo
  • Xu, Chengjie

Abstract

In this paper we study the existence of nontrivial solutions for an impulsive fractional differential equation with Dirichlet boundary conditions. By using Morse theory coupled with local linking arguments, we obtain some new criteria to guarantee that the impulsive fractional differential equations have at least one nontrivial solution.

Suggested Citation

  • Zhao, Yulin & Chen, Haibo & Xu, Chengjie, 2017. "Nontrivial solutions for impulsive fractional differential equations via Morse theory," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 170-179.
    • Handle: RePEc:eee:apmaco:v:307:y:2017:i:c:p:170-179
    DOI: 10.1016/j.amc.2017.02.045
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. Hongxia Shi & Haibo Chen, 2016. "Multiplicity results for a class of boundary value problems with impulsive effects," Mathematische Nachrichten, Wiley Blackwell, vol. 289(5-6), pages 718-726, April.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    4. 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.
    5. Nyamoradi, Nemat & Rodríguez-López, Rosana, 2015. "On boundary value problems for impulsive fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 874-892.
    6. Jia, Mei & Liu, Xiping, 2014. "Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 313-323.
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    Cited by:

    1. Youzheng Ding & Jiafa Xu & Zhengqing Fu, 2019. "Positive Solutions for a System of Fractional Integral Boundary Value Problems of Riemann–Liouville Type Involving Semipositone Nonlinearities," Mathematics, MDPI, vol. 7(10), pages 1-19, October.
    2. Yulin Zhao & Jiafa Xu & Haibo Chen, 2019. "Variational Methods for an Impulsive Fractional Differential Equations with Derivative Term," Mathematics, MDPI, vol. 7(10), pages 1-15, September.

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