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Even homoclinic orbits for super quadratic Hamiltonian systems
Author(s) -
Ding Jian,
Xu Junxiang,
Zhang Fubao
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1298
Subject(s) - homoclinic orbit , mathematics , hamiltonian system , quadratic equation , hamiltonian (control theory) , infinity , boundary value problem , pure mathematics , mathematical analysis , order (exchange) , mathematical physics , combinatorics , bifurcation , physics , geometry , quantum mechanics , mathematical optimization , finance , nonlinear system , economics
We study the existence of even homoclinic orbits for the second‐order Hamiltonian system ü + V u ( t, u )=0. Let V ( t, u )=− K ( t, u )+ W ( t, u )∈ C 1 (ℝ × ℝ n , ℝ), where K is less quadratic and W is super quadratic in u at infinity. Since the system we considered is neither autonomous nor periodic, the ( PS ) condition is difficult to check when we use the Mountain Pass theorem. Therefore, we approximate the homoclinic orbits by virtue of the solutions of a sequence of nil‐boundary‐value problems. Copyright © 2010 John Wiley & Sons, Ltd.
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