Heteroclinic orbits for a discrete pendulum equation
Huafeng Xiao, Jianshe Yu · The Journal of Difference Equations and Applications · 2011
About 20 years ago, Rabinowitz showed that there exist heteroclinic orbits of autonomous Hamiltonian systems joining two equilibria. A special case of autonomous Hamiltonian systems 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 .