Superquadratic or asymptotically quadratic Hamiltonian systems: ground state homoclinic orbits

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• 作者：Guan-Wei Chen
• 关键词：Second ; order Hamiltonian systems ; Ground state homoclinic orbits ; Superquadratic ; Asymptotically quadratic ; Strongly indefinite functionals ; 37J45 ; 37K05 ; 58E05
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：194
• 期：3
• 页码：903-918
• 全文大小：470 KB
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• 作者单位：Guan-Wei Chen (1)
  
  1. School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, Henan Province, P. R. China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1618-1891

文摘

Under super or asymptotically quadratic assumptions at infinity, we obtain the existence of nontrivial ground state homoclinic orbits for a class of second-order Hamiltonian systems with general potentials by a variant generalized weak linking theorem. For the asymptotically quadratic case, a necessary and sufficient condition is obtained for the existence of nontrivial homoclinic orbits. For the superquadratic case, we use general superquadratic conditions to replace the Ambrosetti–Rabinowitz condition.