scholarly journals Existence and Multiplicity of Homoclinic Orbits for Second-Order Hamiltonian Systems with Superquadratic Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Ying Lv ◽  
Chun-Lei Tang
Keyword(s):  
Hamiltonian Systems ◽  
Mountain Pass Theorem ◽  
Homoclinic Orbits ◽  
Second Order ◽  
Mountain Pass ◽  
Fountain Theorem ◽  
Existence And Multiplicity ◽  
Second Order Hamiltonian Systems ◽  
Superquadratic Potential

We investigate the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems with local superquadratic potential by using the Mountain Pass Theorem and the Fountain Theorem, respectively.

Existence of infinitely many homoclinic orbits in Hamiltonian systems

2011 ◽  
Vol 141 (5) ◽  
pp. 1103-1119 ◽  
Author(s):  
X. H. Tang ◽  
Xiaoyan Lin
Keyword(s):  
Potential Function ◽  
Hamiltonian Systems ◽  
Mountain Pass Theorem ◽  
Homoclinic Orbits ◽  
Second Order ◽  
Mountain Pass ◽  
Symmetric Mountain Pass Theorem ◽  
Second Order Hamiltonian Systems ◽  
Existence Criteria

By using the symmetric mountain pass theorem, we establish some new existence criteria to guarantee that the second-order Hamiltonian systems ü(t) − L(t)u(t) + ∇W(t,u(t)) = 0 have infinitely many homoclinic orbits, where t ∈ ℝ, u ∈ ℝN, L ∈ C(ℝ, ℝN × N) and W ∈ C1(ℝ × ℝN, ℝ) are not periodic in t. Our results generalize and improve some existing results in the literature by relaxing the conditions on the potential function W(t, x).

Existence of homoclinic solutions for a class of second-order non-autonomous Hamiltonian systems

2012 ◽  
Vol 62 (5) ◽  
Author(s):  
Qiongfen Zhang ◽  
X. Tang
Keyword(s):  
Hamiltonian Systems ◽  
Mountain Pass Theorem ◽  
Second Order ◽  
Homoclinic Solutions ◽  
Mountain Pass ◽  
Second Order Hamiltonian Systems

AbstractBy using the variant version of Mountain Pass Theorem, the existence of homoclinic solutions for a class of second-order Hamiltonian systems is obtained. The result obtained generalizes and improves some known works.

scholarly journals Homoclinic Orbits for Second-Order Hamiltonian Systems with Some Twist Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Qi Wang ◽  
Qingye Zhang
Keyword(s):  
Hamiltonian Systems ◽  
Linear Growth ◽  
Homoclinic Orbits ◽  
Positive Definite ◽  
Second Order ◽  
Existence And Multiplicity ◽  
Second Order Hamiltonian Systems ◽  
Twist Condition

We study the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systemsq¨−L(t)q+∇qW(t,q)=0, whereL(t)is unnecessarily positive definite for allt∈ℝ, and∇qW(t,q)is of at most linear growth and satisfies some twist condition between the origin and the infinity.

scholarly journals Homoclinic Orbits for a Class of Subquadratic Second Order Hamiltonian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Li-Li Wan
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Orbits ◽  
Second Order ◽  
Existence And Multiplicity ◽  
Second Order Hamiltonian Systems

The existence and multiplicity of homoclinic orbits are considered for a class of subquadratic second order Hamiltonian systems q¨t-Ltqt+∇Wt,qt=0. Recent results from the literature are generalized and significantly improved. Examples are also given in this paper to illustrate our main results.

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