Variational Approach to Homoclinic Solutions for Fractional Hamiltonian Systems

2017 ◽  
Vol 174 (1) ◽  
pp. 223-237
Author(s):  
Nemat Nyamoradi ◽  
Yong Zhou ◽  
Bashir Ahmad ◽  
Ahmed Alsaedi
Keyword(s):  
Hamiltonian Systems ◽  
Variational Approach ◽  
Homoclinic Solutions ◽  
Fractional Hamiltonian Systems

scholarly journals Multiplicity of Homoclinic Solutions for Fractional Hamiltonian Systems with Subquadratic Potential

Entropy ◽  
2017 ◽  
Vol 19 (2) ◽  
pp. 50 ◽  
Author(s):  
Neamat Nyamoradi ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Yong Zhou
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Solutions ◽  
Fractional Hamiltonian Systems

scholarly journals Homoclinic solutions for fractional Hamiltonian systems with indefinite conditions

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2403-2419
Author(s):  
Ziheng Zhang ◽  
Torres Ledesma ◽  
Rong Yuanc
Keyword(s):  
Hamiltonian Systems ◽  
Symmetric Matrix ◽  
Homoclinic Solutions ◽  
Fountain Theorem ◽  
Fractional Hamiltonian Systems ◽  
Variant Fountain Theorem

In this paper we are concerned with the existence of infinitely many homoclinic solutions for the following fractional Hamiltonian systems {-tD??(-?D?tu(t))-L(t)u(t) + ?W(t,u(t)) = 0, u ? H?(R,Rn), (FHS) where ? ? (1/2,1), t ? R, u ? Rn, L ? C(R,Rn2) is a symmetric matrix for all t ? R, W ? C1(R x Rn,R) and ?W(t,u) is the gradient of W(t,u) at u. The novelty of this paper is that, when L(t) is allowed to be indefinite and W(t,u) satisfies some new superquadratic conditions, we show that (FHS) possesses infinitely many homoclinic solutions via a variant fountain theorem. Recent results are generalized and significantly improved.

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