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In this paper, we give several new sufficient conditions for the existence of infinitely many homoclinic orbits of the second-order ordinary $p$-Laplacian system $$ \frac{d}{dt}\left(|\dot{u}(t)|^{p-2}\dot{u}(t)\right)-a(t)|u(t)|^{p-2}u(t)+\nabla W(t, u(t))=0, $$ where $p>1, \ t\in {\mathbb{R}},\ u\in {\mathbb{R}}^{N}$, $a\in C({\mathbb{R}}, {\mathbb{R}})$ and $W\in C^{1}({\mathbb{R}}\times {\mathbb{R}}^{N}, {\mathbb{R}})$ are no periodic in $t$, which greatly improve the known results due to Rabinowitz and Willem.

INFINITELY MANY HOMOCLINIC ORBITS OF SECOND-ORDER $p$-LAPLACIAN SYSTEMS