The existence and multiplicity of homoclinic solutions are obtained for Hamiltonian systems of p-Laplacian-like type \(\frac{d}{dt}(\varphi (t,{\dot{u}}))-a(t)|u(t)|^{p-2}u(t)+\lambda \nabla W(t,u(t))=0\) via variational methods, where a(t) is bounded and W(t, u) is under concave-convex conditions. Recent results in the literature are generalized and improved significantly.

中文翻译：

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p-Laplacian-Like型哈密顿系统的同宿解

对于p -Laplacian型\（\ frac {d} {dt}（\ varphi（t，{\ dot {u}}））-a（t）|的哈密​​顿系统，获得了同宿解的存在性和多重性。 u（t）| ^ {p-2} u（t）+ \ lambda \ nabla W（t，u（t））= 0 \）通过变分方法，其中a（t）有界，W（t，  u）在凹凸条件下。文献中的最新结果得到了概括和显着改善。