Abstract

We are concerned with conservative systems q = del V(q), q is an element of R-N for a general class of potentials V is an element of C-1(R-N). Assuming that a given sublevel set {V = c} splits in the disjoint union of two closed subsets V--(c) and V-+(c), for some c is an element of R, we establish the existence of bounded solutions q(c) to the above system with energy equal to -c whose trajectories connect V--(c) and V-+(c). The solutions are obtained through an energy constrained variational method, whenever mild coerciveness properties are present in the problem. The connecting orbits are classified into brake, heteroclinic or homoclinic type, depending on the behavior of del V on partial derivative V-+/-(c). Next, we illustrate applications of the existence result to double-well potentials V, and for potentials associated to systems of duffing type and of multiple-pendulum type. In each of the above cases we prove some convergence results of the family of solutions (q(c)).