Results 21 to 30 of about 9,595 (205)

Multiplicity of Homoclinic Solutions for Fractional Hamiltonian Systems with Subquadratic Potential

Entropy, 2017
In this paper, we study the existence of homoclinic solutions for the fractional Hamiltonian systems with left and right Liouville–Weyl derivatives. We establish some new results concerning the existence and multiplicity of homoclinic solutions for the ...
Neamat Nyamoradi, Ahmed Alsaedi, Bashir Ahmad, Yong Zhou   +3 more
doaj   +1 more source

Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators

Shock and Vibration, 2016
The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure.
Yang-Yang Chen, Shu-Hui Chen, Wei-Wei Wang   +2 more
doaj   +1 more source

Topology and Homoclinic Trajectories of Discrete Dynamical Systems [PDF]

, 2012
We show that nontrivial homoclinic trajectories of a family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circle bifurcate from a stationary solution if the asymptotic stable bundles Es(+{\infty}) and Es(-{\infty}) of ...
A. Abbondandolo, A. Abbondandolo, A. G. Baskakov, C. Pötzsche, C. Pötzsche, C. Pötzsche, D. Husemoller, J. Pejsachowicz, J. Pejsachowicz, J. Pejsachowicz, J. Pejsachowicz, J. Pejsachowicz, Jacobo Pejsachowicz, M. F. Atiyah, M. G. Crandall, M. Rasmussen, P. Benevieri, P. Benevieri, P. M. Fitzpatrick, R. J. Sacker, Robert Skiba, S. Lang, T. Bartsch, T. Kato, Y. Hamaya   +24 more
core   +2 more sources

Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction [PDF]

, 2007
We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers.
Bernardo Sánchez-rey B, Escuela Universitaria Politécnica, Guillaume James A, Jesus Cuevas B   +3 more
core   +5 more sources

Infinitely many homoclinic solutions for a class of damped vibration problems

Electronic Journal of Qualitative Theory of Differential Equations, 2022
In this paper, we consider the multiplicity of homoclinic solutions for the following damped vibration problems $$ \ddot{x}(t)+B\dot{x}(t)-A(t)x(t)+H_{x}(t,x(t))=0,$$ where $A(t)\in (\mathbb{R},\mathbb{R}^{N})$ is a symmetric matrix for all $t\in \mathbb{
Huijuan Xu, Shan Jiang, Guanggang Liu
doaj   +1 more source

Homoclinic Solutions for Fourth Order Traveling Wave Equations [PDF]

SIAM Journal on Mathematical Analysis, 2009
We consider homoclinic solutions of fourth order equations $$ u^{""} + ^2 u^{"} + V_u (u)=0 {in} \R ,$$ where $V(u)$ is either the suspension bridge type $V(u)=e^u-1-u$ or Swift-Hohenberg type $ V(u)= {1/4}(u^2-1)^2$. For the suspension bridge type equation, we prove existence of a homoclinic solution for {\em all} $ \in (0, _*)$ where $ _ ...
Santra, Sanjiban, Wei, Juncheng
openaire   +2 more sources

Homoclinic Solutions for a Second-Order Nonperiodic Asymptotically Linear Hamiltonian Systems

Abstract and Applied Analysis, 2013
We establish a new existence result on homoclinic solutions for a second-order nonperiodic Hamiltonian systems. This homoclinic solution is obtained as a limit of solutions of a certain sequence of nil-boundary value problems which are obtained by the ...
Qiang Zheng
doaj   +1 more source

Homoclinic Orbits In Slowly Varying Oscillators [PDF]

, 1987
We obtain existence and bifurcation theorems for homoclinic orbits in three-dimensional flows that are perturbations of families of planar Hamiltonian systems. The perturbations may or may not depend explicitly on time.
Holmes, Philip, Wiggins, Stephen
core   +1 more source

Homoclinic Solutions of Hamiltonian Systems with Symmetry

Journal of Differential Equations, 1999
Consider a Hamiltonian system with a Hamiltonian of the following form: \[ H(z,t)=\tfrac{1}{2}Az\cdot z+F(z,t). \] The authors show that if (i) the spectrum of the matrix \(JA\) (where \(J\) is the standard symplectic matrix) does not intersect the imaginary axis; (ii) \(F\) is invariant under the action of a compact Lie group; and (iii) \(F\) is ...
ARIOLI, GIANNI, A. Szulkin
openaire   +2 more sources

On Existence of Infinitely Many Homoclinic Solutions

Monatshefte f�r Mathematik, 2000
Using the concept of an isolating segment, some sufficient conditions for the existence of homoclinic solutions to nonautonomous ODEs are obtained. As an application it is shown that for all sufficiently small \(\varepsilon >0\) there exist infinitely many geometrically distinct solutions homoclinic to the trivial solution \(z=0\) to the equation ...
Wójcik, Klaudiusz, Zgliczyński, Piotr
openaire   +2 more sources