Homoclinic Solutions for Hamiltonian Systems of p-Laplacian-Like Type

Abstract

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.