Existence of three solution for fractional Hamiltonian system
DOI:
https://doi.org/10.17268/sel.mat.2017.01.06Keywords:
Fractional calculus, fractional derivatives, fractional Hamiltonian system, boundary value problemAbstract
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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