Existencia de tres soluciones para el sistema hamiltoniano fraccionario

• Autores: César Torres Ledesma, Oliverio Pichardo Diestra
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 4, Nº. 1, 2017 (Ejemplar dedicado a: Enero - Julio), págs. 51-58
• Idioma: español
• DOI: 10.17268/sel.mat.2017.01.06
• Títulos paralelos:
  • Existence of three solution for fractional Hamiltonian system
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• Resumen
  • español

    En este artículo se considera un sistema Hamiltoniano dado por:(0.1)              −tDα T(0Dα t u(t)) = ∇F(t,u(t)), a.e t ∈ [0,T]                       u(0) = u(T) = 0.donde α ∈ (1/2,1), t ∈ [0,T], u ∈ Rn, F : [0,T]×Rn → R es una función dada y ∇F(t,u) es el gradiente de F en u. La novedad de este trabajo es que, usando una versión modificada del teorema del paso de montaña para funcional limitada desde abajo probamos la existencia de por lo menos tres soluciones para (0.1).

  • English

    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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