Homoclinic solutions for a class of second order Hamiltonian systems. Issue 8 (16th March 2015)

• Record Type: Journal Article
• Authors: Zhang, Qingye
• Is Part Of: Mathematische Nachrichten. Volume 288:Issue 8/9(2015)
• Page Start: 1073
• Page End: 1081
• Publication Date: 2015-03-16
• Subjects: Hamiltonian system -- homoclinic solution -- variational method -- 34C37 -- 58E30 -- 37J45; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201200293
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : In this paper, we study homoclinic solutions for the nonperiodic second order Hamiltonian systems u ̈ − L ( t ) u + W u ( t, u ) = 0, ∀ t ∈ R, where L is unnecessarily coercive or uniformly positively definite, and W ( t, u ) is only locally defined near the origin with respect to u . Under some general conditions on L and W, we show that the above system has infinitely many homoclinic solutions near the origin. Some related results in the literature are extended and generalized.