Multiple Solutions for a Class of Fractional Hamiltonian Systems

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Jiafa Xu ◽  
Donal O'Regan ◽  
Keyu Zhang
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Multiple Solutions ◽  
Existence Theorems ◽  
Fractional Hamiltonian Systems

AbstractIn this paper, we establish two existence theorems for multiple solutions for the following fractional Hamiltonian systemwhere

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.

Hamiltonian systems of Schrödinger equations with vanishing potentials

2020 ◽  
pp. 2050074
Author(s):  
E. Toon ◽  
P. Ubilla
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Positive Solutions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Cerami Sequence ◽  
Cerami Sequences ◽  
Vanishing Potentials

In this paper, by means of minimax techniques involving Cerami sequences, we prove the existence of at least one pair of positive solutions for a Hamiltonian system of Schrödinger equations in [Formula: see text] with potentials vanishing at infinity and subcritical nonlinearities which are superlinear at the origin and at infinity. We establish new estimates to prove the boundedness of a Cerami sequence.

scholarly journals The number of limit cycles for a class of quintic Hamiltonian systems under quintic perturbations

2002 ◽  
Vol 73 (1) ◽  
pp. 37-54 ◽  
Author(s):  
Guowei Chen ◽  
Yongbin Wu ◽  
Xinan Yang
Keyword(s):  
Hopf Bifurcation ◽  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Limit Cycles ◽  
Homoclinic Bifurcation

AbstractThe Hopf bifurcation and homoclinic bifurcation of the quintic Hamiltonian system is analyzed under quintic perturbations by using unfolding theory in this paper. We show that a quintic system can have at least 29 limit cycles.

scholarly journals Higher Order Hamiltonian Systems with Generalized Legendre Transformation

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 163
Author(s):  
Dana Smetanová
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Higher Order ◽  
Second Order ◽  
Legendre Transformation ◽  
Lagrange Equations ◽  
Hamilton Equations ◽  
Strongly Regular

The aim of this paper is to report some recent results regarding second order Lagrangians corresponding to 2nd and 3rd order Euler–Lagrange forms. The associated 3rd order Hamiltonian systems are found. The generalized Legendre transformation and geometrical correspondence between solutions of the Hamilton equations and the Euler–Lagrange equations are studied. The theory is illustrated on examples of Hamiltonian systems satisfying the following conditions: (a) the Hamiltonian system is strongly regular and the Legendre transformation exists; (b) the Hamiltonian system is strongly regular and the Legendre transformation does not exist; (c) the Legendre transformation exists and the Hamiltonian system is not regular but satisfies a weaker condition.

Sign in / Sign up

Export Citation Format

Share Document