Minimal heteroclinics for a class of fourth order O.D.E. systems

TL;DR

This paper proves the existence of minimal heteroclinic orbits in a class of fourth order O.D.E. systems with variational structure, where equilibria form manifolds and heteroclinics connect different components.

Contribution

It establishes the existence of minimal heteroclinic orbits for a broad class of fourth order O.D.E. systems with complex equilibrium structures.

Findings

Existence of heteroclinic orbits connecting disjoint equilibrium manifolds.

Application of variational methods to fourth order O.D.E. systems.

Framework applicable to systems with manifold equilibria.

Abstract

We prove the existence of minimal heteroclinic orbits for a class of fourth order O.D.E. systems with variational structure. In our general set-up, the set of equilibria of these systems is a union of manifolds, and the heteroclinic orbits connect two disjoint components of this set.