Parabolic Orbits for a Class of Singular Hamiltonian Systems with a Fixed Energy

TL;DR

This paper proves the existence of parabolic orbits in certain singular Hamiltonian systems with fixed energy by using a limit process on non-collision periodic solutions derived via the Mountain Pass Lemma.

Contribution

It introduces a novel approach to establish parabolic orbits for singular Hamiltonian systems through a limiting process of periodic solutions.

Findings

Existence of parabolic orbits in specified Hamiltonian systems.

Application of Mountain Pass Lemma to find non-collision periodic solutions.

Convergence of periodic solutions to parabolic orbits.

Abstract

The existence of parabolic orbits is obtained for a class of singular Hamiltonian systems $\ddot{u}(t)+\nabla V(u(t))=0$ by taking limit for a sequence of non-collision periodic solutions which are obtained by Mountain Pass Lemma.