Infinitely Many Homoclinic Solutions for a Class of Indefinite Perturbed Second-Order Hamiltonian Systems
3673-3690
2016-10
en
research_article
In this paper, we study the existence of infinitely many homoclinic solutions of the perturbed second-order Hamiltonian system -u¨(t)+L(t)u=Wu(t,u(t))+Gu(t,u(t)),where L(t) and W(t,u) are neither autonomous nor periodic in t. Under the assumptions that W(t,u) is indefinite in sign and only locally superquadratic as |u|→+∞ and G(t,u) is not even in u, we prove the existence of infinitely many homoclinic solutions in spite of the lack of the symmetry of this problem by Bolle’s perturbation method in critical point theory. Our results generalize some known results and are even new in the symmetric case.
articles
2019-04-10T19:01
false
2016-10-01
https://scigraph.springernature.com/explorer/license/
http://link.springer.com/10.1007/s00009-016-0708-6
pub.1007922458
dimensions_id
Zhang
Liang
10.1007/s00009-016-0708-6
doi
Pure Mathematics
Mathematical Sciences
Tang
Xianhua
University of Jinan
School of Mathematical Sciences, University of Jinan, 250022, Jinan, Shangdong, People’s Republic of China
Mediterranean Journal of Mathematics
1660-5446
1660-5454
Springer Nature - SN SciGraph project
School of Mathematics and Statistics, Central South University, 410083, Changsha, Hunan, People’s Republic of China
Central South University
Chen
Yi
China University of Mining and Technology
Department of Mathematics, China University of Mining and Technology, 221116, Xuzhou, Jiangsu, People’s Republic of China
5
25bd871abbb53113dca57d154b597b5a7262d40f4c0735a4519f3124403d0b35
readcube_id
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