Existence and multiplicity of homoclinic orbits of a second-orderdifferential difference equation via variational methods

Authors: C. Guo, D. O’Regan, Y. Xu, R. P. Agarwal

Keywords: homoclinic solutions; differential difference equation; critical point theory

Abstract:

This paper is concerned with the existence of homoclinic orbits of the second order differential difference equation q(t)−Kq(t,q(t))+ f (t,q(t +τ),q(t),q(t −τ)) = h(t). By using critical point theory and variational methods, a nontrivial homoclinic orbit is obtained as a limit of a certain sequence of periodic solutions of an appropriate equation. As a result, we generalize the results obtained by Smets and Willem. Also, by applying a Symmetric Mountain Pass Lemma, we obtain infinitely many homoclinic orbits of the above equation.

References:

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