Homoclinic solutions for some second order non-autonomous Hamiltonian systems without the globally superquadratic condition

✍ Scribed by Ziheng Zhang; Rong Yuan

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 646 KB
• Volume: 72
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2009.09.022

✦ Synopsis

This paper deals with the existence of homoclinic solutions for the following second order non-autonomous Hamiltonian system

where

is not globally superquadratic on q and some additionally reasonable assumptions, we give a new existence result to guarantee that (HS) has a homoclinic solution q(t) emanating from 0. The homoclinic solution q(t) is obtained as a limit of 2kT -periodic solutions of a sequence of the second order differential equations and these periodic solutions are obtained by the use of a standard version of the Mountain Pass Theorem. Recent results in the literature are generalized and significantly improved.