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Ground State Solutions for a Class of Fractional Differential Equations with Dirichlet Boundary Value Condition

Author

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  • Zhigang Hu
  • Wenbin Liu
  • Jiaying Liu

Abstract

In this paper, we apply the method of the Nehari manifold to study the fractional differential equation (d/dt)((12/) 0Dt-β(u′(t))+(12/) tDT-β(u′(t)))= f(t,u(t)), a.e. t ∈ [0, T], and u(0) = u(T) = 0, where 0Dt-β, tDT-β are the left and right Riemann‐Liouville fractional integrals of order 0 ≤ β

Suggested Citation

  • Zhigang Hu & Wenbin Liu & Jiaying Liu, 2014. "Ground State Solutions for a Class of Fractional Differential Equations with Dirichlet Boundary Value Condition," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:958420
    DOI: 10.1155/2014/958420
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    References listed on IDEAS

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    1. Zuoshi Xie & Yuanfeng Jin & Chengmin Hou, 2012. "Multiple Solutions for a Fractional Difference Boundary Value Problem via Variational Approach," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, December.
    2. Chuanzhi Bai, 2012. "Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Zuoshi Xie & Yuanfeng Jin & Chengmin Hou, 2012. "Multiple Solutions for a Fractional Difference Boundary Value Problem via Variational Approach," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Jing Chen & X. H. Tang, 2012. "Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Chuanzhi Bai, 2012. "Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, September.
    6. Jing Chen & X. H. Tang, 2012. "Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-21, January.
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