47 research outputs found
Multibump solutions of a class of second-order discrete Hamiltonian systems
For a class of second-order discrete Hamiltonian systems
, we investigate the existence of
homoclinic orbits by applying variational method, where and
are periodic functions. Further, we show that there exist either uncountable
many homoclinic orbits or multibump solutions under certain conditions
Heteroclinic Orbits for a Discrete Pendulum Equation
About twenty years ago, Rabinowitz showed firstly that there exist
heteroclinic orbits of autonomous Hamiltonian system joining two equilibria. A
special case of autonomous Hamiltonian system is the classical pendulum
equation. The phase plane analysis of pendulum equation shows the existence of
heteroclinic orbits joining two equilibria, which coincide with the result of
Rabinowitz. However, the phase plane of discrete pendulum equation is similar
to that of the classical pendulum equation, which suggests the existence of
heteroclinic orbits for discrete pendulum equation also. By using variational
method and delicate analysis technique, we show that there indeed exist
heteroclinic orbits of discrete pendulum equation joining every two adjacent
points of
A Variant of the Mountain Pass Theorem and Variational Gluing
none2siThis paper surveys some recent work on a variant of the Mountain Pass Theorem that is applicable to some classes of differential equations involving unbounded spatial or temporal domains. In particular its application to a system of semilinear elliptic PDEs on and to a family of Hamiltonian systems involving double well potentials will also be discussed.openMontecchiari, Piero; Rabinowitz, Paul H.Montecchiari, Piero; Rabinowitz, Paul H
Interfering Solutions of a Nonhomogeneous Hamiltonian System
A Hamiltonian system is studied which has a term approaching a constant at an exponential rate at infinity. A minimax argument is used to show that the equation has a positive homoclinic solution. The proof employs the interaction between translated solutions of the corresponding homogeneous equation. What distinguishes this result from its few predecessors is that the equation has a nonhomogeneous nonlinearity
Chaotic orbits for systems of nonlocal equations
We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinc, homoclinic and chaotic trajectories are constructed