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Homoclinic solutions for a class of second order Hamiltonian systems
Author(s) -
Zhang Qingye
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200293
Subject(s) - homoclinic orbit , mathematics , hamiltonian system , hamiltonian (control theory) , class (philosophy) , order (exchange) , pure mathematics , mathematical analysis , nonlinear system , mathematical optimization , bifurcation , physics , finance , quantum mechanics , artificial intelligence , computer science , economics
In this paper, we study homoclinic solutions for the nonperiodic second order Hamiltonian systemsu ̈ − 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.