Existence of three solution for fractional Hamiltonian system


  • César Torres Ledesma
  • Oliverio Pichardo Diestra




Fractional calculus, fractional derivatives, fractional Hamiltonian system, boundary value problem


In this paper we consider the fractional Hamiltonian system given by

(0.1)                       −tDα T(0Dα t u(t)) = ∇F(t,u(t)), a.e t ∈ [0,T]

                                 u(0) = u(T) = 0.

where α ∈ (1/2,1), t ∈ [0,T], u ∈Rn, F : [0,T]×Rn →R is a given function and ∇F(t,u) is the gradient of F at u. The novelty of this paper is that, using a modified version of mountain pass theorem for functional bounded from below we prove the existence of at least three solutions for (0.2). 


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How to Cite

Torres Ledesma, C., & Pichardo Diestra, O. (2017). Existence of three solution for fractional Hamiltonian system. Selecciones Matemáticas, 4(01), 51-58. https://doi.org/10.17268/sel.mat.2017.01.06