Subharmonics and homoclinics for a class of Hamiltonian-like equations
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Submission date: 20. Jul. 2009 (revised version: September 2009)
MSC-Numbers: 34C25, 34C37, 37K60
Keywords and phrases: Advanced-delayed differential equations, critical point theory, periodic and homoclinic solutions
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We study the existence of periodic and homoclinic solutions for a class of non-autonomous second order advanced-delayed differential equations of the type
We prove, under some growth conditions on the non-linearities, the existence of non-constant periodic solutions with period any given positive integer. Using very simple arguments, the existence of a non-trivial homoclinic solution is also established. This homoclinic is obtained as the limit of subharmonics. An application to the existence of periodic and homoclinic travelling waves in an infinite lattice of partciles with N-nearest-neighbour interaction and on-site potential is given.