scholarly journals Homoclinic solutions for eventually autonomous high-dimensional Hamiltonian systems

2002 ◽  
Vol 274 (2) ◽  
pp. 536-553
Author(s):  
B. Buffoni
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Solutions ◽  
High Dimensional

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 Multiple homoclinic solutions for a class of nonhomogeneous Hamiltonian systems

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Chunhua Deng ◽  
Dong-Lun Wu
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Solutions

Homoclinic solutions for second order impulsive Hamiltonian systems with small forcing terms

2016 ◽  
Vol 39 (18) ◽  
pp. 5570-5581
Author(s):  
Lizhao Yan ◽  
Fei Xu ◽  
Mingyong Lai
Keyword(s):  
Hamiltonian Systems ◽  
Second Order ◽  
Homoclinic Solutions

scholarly journals Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ziheng Zhang ◽  
Fang-Fang Liao ◽  
Patricia J. Y. Wong
Keyword(s):  
Hamiltonian Systems ◽  
Bounded Function ◽  
Homoclinic Solution ◽  
Second Order ◽  
Homoclinic Solutions ◽  
Global Maximum ◽  
Continuous Bounded Function ◽  
Almost Periodic ◽  
Strong Force ◽  
Singular Hamiltonian Systems

We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systemsu¨+atWuu=0, (HS) where-∞<t<+∞,u=u1,u2, …,uN∈ℝNN≥3,a:ℝ→ℝis a continuous bounded function, and the potentialW:ℝN∖{ξ}→ℝhas a singularity at0≠ξ∈ℝN, andWuuis the gradient ofWatu. The novelty of this paper is that, for the case thatN≥3and (HS) is nonautonomous (neither periodic nor almost periodic), we show that (HS) possesses at least one nontrivial homoclinic solution. Our main hypotheses are the strong force condition of Gordon and the uniqueness of a global maximum ofW. Different from the cases that (HS) is autonomousat≡1or (HS) is periodic or almost periodic, as far as we know, this is the first result concerning the case that (HS) is nonautonomous andN≥3. Besides the usual conditions onW, we need the assumption thata′t<0for allt∈ℝto guarantee the existence of homoclinic solution. Recent results in the literature are generalized and significantly improved.

Infinitely many homoclinic solutions for second-order discrete Hamiltonian systems

2013 ◽  
Vol 19 (12) ◽  
pp. 1940-1951 ◽  
Author(s):  
Huiwen Chen ◽  
Zhimin He
Keyword(s):  
Hamiltonian Systems ◽  
Second Order ◽  
Homoclinic Solutions

Multiplicity and concentration of homoclinic solutions for some second order Hamiltonian systems

2015 ◽  
Vol 114 ◽  
pp. 105-115 ◽  
Author(s):  
Juntao Sun ◽  
Tsung-fang Wu
Keyword(s):  
Hamiltonian Systems ◽  
Second Order ◽  
Homoclinic Solutions ◽  
Second Order Hamiltonian Systems

scholarly journals On diffusion in high-dimensional Hamiltonian systems

2005 ◽  
Vol 229 (1) ◽  
pp. 1-61 ◽  
Author(s):  
Jean Bourgain ◽  
Vadim Kaloshin
Keyword(s):  
Hamiltonian Systems ◽  
High Dimensional
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