HOMOCLINIC ORBITS FOR A CLASS OF HAMILTONIAN SYSTEMS WITH SUPERQUADRATIC OR ASYMPTOTICALLY QUADRATIC POTENTIALS

摘要

In this paper we study the following nonperiodic second order Hamiltonian system where the matrix L(t) 2 C(R;R~N~2 ) and R(t; u) is asymptotically quadratic or super quadratic in u as juj ! 1. Under more general assumptions on the matrix L(t), if R is superquadratic and even in u, we obtain in nitely many homoclinic orbits. On the other hand, if R is asymptotically quadratic, we also prove the existence and multiplicity of homoclinic orbits for the above system.