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Homoclinic orbits for Hamiltonian systems induced by impulses
Author(s) -
Xie Jingli,
Luo Zhiguo
Publication year - 2016
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.3636
Subject(s) - homoclinic orbit , mathematics , hamiltonian system , laplace operator , hamiltonian (control theory) , mountain pass theorem , heteroclinic orbit , operator (biology) , homoclinic bifurcation , mathematical analysis , pure mathematics , mathematical physics , bifurcation , physics , mathematical optimization , nonlinear system , quantum mechanics , biochemistry , chemistry , repressor , transcription factor , gene
In this paper, we consider a class of impulsive Hamiltonian systems with a p ‐Laplacian operator. Under certain conditions, we establish the existence of homoclinic orbits by means of the mountain pass theorem and an approximation technique. In some special cases, the homoclinic orbits are induced by the impulses in the sense that the associated non‐impulsive systems admit no non‐trivial homoclinic orbits. Copyright © 2015 John Wiley & Sons, Ltd.