Homoclinic orbits of first order discrete Hamiltonian systems with super linear terms

2011 ◽  
Vol 54 (12) ◽  
pp. 2583-2596 ◽  
Author(s):  
WenXiong Chen ◽  
MinBo Yang ◽  
YanHeng Ding
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Orbits ◽  
First Order

Homoclinic Orbits For First Order Hamiltonian Systems With Convex Potentials

2006 ◽  
Vol 6 (3) ◽  
Author(s):  
Xiangjin Xu
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Orbits ◽  
First Order

AbstractIn this paper new estimates on the C

scholarly journals Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Xiaoyan Lin ◽  
Qi-Ming Zhang ◽  
X. H. Tang
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Satisfying Condition ◽  
Sufficient Conditions ◽  
Homoclinic Orbits ◽  
First Order ◽  
Nonlinear Hamiltonian System

We give several sufficient conditions under which the first-order nonlinear Hamiltonian systemx'(t)=α(t)x(t)+f(t,y(t)),  y'(t)=-g(t,x(t))-α(t)y(t)has no solution(x(t),y(t))satisfying condition0<∫-∞+∞[|x(t)|ν+(1+β(t))|y(t)|μ]dt<+∞‍,whereμ,ν>1and(1/μ)+(1/ν)=1,0≤xf(t,x)≤β(t)|x|μ,xg(t,x)≤γ0(t)|x|ν,β(t),γ0(t)≥0, andα(t)are locally Lebesgue integrable real-valued functions defined onℝ.

scholarly journals Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Long Yuhua
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Mountain Pass Theorem ◽  
Homoclinic Orbits ◽  
Existence Results ◽  
Mountain Pass ◽  
First Order ◽  
Discrete Hamiltonian System ◽  
Generalized Mountain Pass Theorem

A class of first-order noncoercive discrete Hamiltonian systems are considered. Based on a generalized mountain pass theorem, some existence results of homoclinic orbits are obtained when the discrete Hamiltonian system is not periodical and need not satisfy the global Ambrosetti-Rabinowitz condition.

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