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摘要
In this paper we study the following nonperiodic second order Hamiltonian system -u(t) + L(t)u(t) = del R-u(t, u(t)), for all (t, u) is an element of R x R-N, where the matrix L(t) is an element of C(R, R-N2) and R(t, u) is asymptotically quadratic or super quadratic in u as vertical bar u vertical bar -> infinity. Under more general assumptions on the matrix L(t), if R is superquadratic and even in u, we obtain in finitely 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.
