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Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory

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  • Jing Chen
  • X. H. Tang

Abstract

We study the existence and multiplicity of solutions for the following fractional boundary value problem: (d/dt)((1/2) 0Dt-β(u′(t))+(1/2) tDT-β(u′(t)))+∇F(t,u(t))=0000, a.e. t∈[,T], u()=u(T)=, where F(t, ·) are superquadratic, asymptotically quadratic, and subquadratic, respectively. Several examples are presented to illustrate our results.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:648635
    DOI: 10.1155/2012/648635
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