Periodic solutions to second order Hamiltonian systems in an unbounded potential well

1987 ◽  
Vol 105 (1) ◽  
pp. 1-15
Author(s):  
C. Greco
Keyword(s):  
Periodic Solutions ◽  
Second Order ◽  
Potential Well ◽  
Second Order Hamiltonian Systems ◽  
Open Set ◽  
Unbounded Potential ◽  
Order Hamiltonian System ◽  
Existence Of Periodic Solutions ◽  
Image Position ◽  
Second Order Hamiltonian System

SynopsisIn this paper we give some results on the existence of periodic solutions to the second order Hamiltonian system:where and Ω is an open set of ℝn with non-empty bounded complement ℝn\Ω; we suppose V(t, x) is periodic in t, V(t, x)→ + ∞ as x → ∂Ω and V is super (or sub)-quadratic as |x| → + ∞.

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.

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.

scholarly journals Periodic Solution of Second-Order Hamiltonian Systems with a Change Sign Potential on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
You-Hui Su ◽  
Wan-Tong Li
Keyword(s):  
Periodic Solution ◽  
Hamiltonian System ◽  
Critical Theory ◽  
Time Scales ◽  
Second Order ◽  
Second Order Hamiltonian Systems ◽  
Minimax Methods ◽  
Order Hamiltonian System ◽  
Second Order Hamiltonian System ◽  
First Time

This paper is concerned with the second-order Hamiltonian system on time scales𝕋of the formuΔΔ(ρ(t))+μb(t)|u(t)|μ−2u(t)+∇¯H(t,u(t))=0, Δ-a.e.t∈[0,T]𝕋 ,u(0)−u(T)=uΔ(ρ(0))−uΔ(ρ(T))=0,where0,T∈𝕋. By using the minimax methods in critical theory, an existence theorem of periodic solution for the above system is established. As an application, an example is given to illustrate the result. This is probably the first time the existence of periodic solutions for second-order Hamiltonian system on time scales has been studied by critical theory.

scholarly journals Periodic Solutions of Some Impulsive Hamiltonian Systems with Convexity Potentials

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Dezhu Chen ◽  
Binxiang Dai
Keyword(s):  
Variational Methods ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Existence Theorems ◽  
Second Order ◽  
Second Order Hamiltonian Systems ◽  
Existence Of Periodic Solutions

We study the existence of periodic solutions of some second-order Hamiltonian systems with impulses. We obtain some new existence theorems by variational methods.

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