Periodic Bounce Solutions of Hamiltonian Systems in Bounded Domains

2007 ◽  
Vol 7 (4) ◽  
Author(s):  
Yong Liu ◽  
Mei-Yue Jiang
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Second Order ◽  
Bounded Domains ◽  
Order Hamiltonian System ◽  
Second Order Hamiltonian System

AbstractPeriodic bounce solutions of the second order Hamiltonian system−x″ = ∇V (x, t), x(t) ∈ Ω̅is studied, where Ω ⊂ ℝ

Orbits with minimal period for a class of autonomous second order one-dimensional Hamiltonian systems

2018 ◽  
Vol 25 (1) ◽  
pp. 117-122 ◽  
Author(s):  
Chouhaïd Souissi
Keyword(s):  
Periodic Solution ◽  
Hamiltonian System ◽  
Variational Method ◽  
Hamiltonian Systems ◽  
Second Order ◽  
Minimal Period ◽  
One Dimensional ◽  
Order Hamiltonian System ◽  
Second Order Hamiltonian System

AbstractWe show, under an iterative condition which is similar to but stronger than that of Ambrosetti and Rabinowitz and by using a variational method, the existence of aT-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential\ddot{z}+V^{\prime}(z)=0,\quad z\in\mathbb{R},for any{T>0}. Moreover, such a solution has{T/k}as a minimal period for some integer{1\leq k\leq 3}.

Odd Homoclinic Orbits for a Second Order Hamiltonian System

2012 ◽  
Vol 12 (1) ◽  
Author(s):  
Liliane A. Maia ◽  
Olimpio H. Miyagaki ◽  
Sergio H. M. Soares
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Homoclinic Orbit ◽  
Homoclinic Orbits ◽  
Second Order ◽  
Concentration Compactness ◽  
Concentration Compactness Principle ◽  
Order Hamiltonian System ◽  
Compactness Principle ◽  
Second Order Hamiltonian System

AbstractThe aim of this paper is to find an odd homoclinic orbit for a class of reversible Hamiltonian systems. The proof is variational and it employs a version of the concentration compactness principle of P. L. Lions in a lemma due to Struwe.

Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Joanna Janczewska ◽  
Jakub Maksymiuk
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Homoclinic Orbits ◽  
Second Order ◽  
Singular Points ◽  
Global Maximum ◽  
Strong Force ◽  
Second Order Hamiltonian Systems ◽  
Order Hamiltonian System ◽  
Second Order Hamiltonian System

AbstractWe consider a conservative second order Hamiltonian system $$\ddot q + \nabla V(q) = 0$$ in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ {0} = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.

Non-constant periodic solutions for second order Hamiltonian system with a p-Laplacian

2012 ◽  
Vol 62 (2) ◽  
Author(s):  
Xingyong Zhang ◽  
Xianhua Tang
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Existence Theorems ◽  
Second Order ◽  
Linking Theorem ◽  
Order Hamiltonian System ◽  
Second Order Hamiltonian System

AbstractIn this paper, some existence theorems are obtained for nonconstant periodic solutions of second order Hamiltonian system with a p-Laplacian by using the Linking Theorem.

Subharmonics near an equilibrium for some second-order Hamiltonian systems

1993 ◽  
Vol 123 (5) ◽  
pp. 819-834 ◽  
Author(s):  
Patricio L. Felmer ◽  
Elves A. de B. e Silva
Keyword(s):  
Hamiltonian System ◽  
Periodic Solutions ◽  
Second Order ◽  
Point Of View ◽  
Subharmonic Solutions ◽  
Second Order Hamiltonian Systems ◽  
Order Hamiltonian System ◽  
Existence Of Periodic Solutions ◽  
Image Position ◽  
Second Order Hamiltonian System

SynopsisThis work is devoted to the study of subharmonic solutions of a second-order Hamiltonian systemnear an equilibrium point, say q = 0. The problem of existence of periodic solutions from the global point of view is also considered.This problem has been studied for the case where the potential is positive and superquadratic. In this work a potential V that has change in sign is considered. The potential is decomposed aswhere P is homogeneous, superquadratic and nondegenerate, and is of higher order near 0. In this paper the existence is shown of a sequence of subharmonic solutions of the equation above that converges to the equilibrium, such that their minimal periods converge to infinity.This problem is approached from a variational point of view. Existence of subharmonic and periodic solutions is obtained via minimax techniques.

Sign in / Sign up

Export Citation Format

Share Document