On a theorem of Weinstein

Abstract

Abstract : This paper contains an existence theorem for a special class of periodic solutions of Hamiltonian systems and generalizes an earlier result of the same nature due to Weinstein. He studied a general class of mechanical systems and established the existence of special kinds of periodic solutions which he called brake orbits. Roughly speaking these solutions start at the boundary of a potential well with 0 velocity and return to the edge of the well, again with 0 velocity, a half period later. This paper contains a generalization of his results using minimax methods form the calculus of variations as the existence tool.