HOMOCLINIC ORBITS OF FIRST-ORDER SUPERQUADRATIC HAMILTONIAN SYSTEMS

作者：Batkam Cyril Joel^*

来源：Discrete and Continuous Dynamical Systems, 2014, 34(9): 3353-3369.

DOI：10.3934/dcds.2014.34.3353

• Hamiltonian system
• homoclinic orbits
• ground state
• generalized fountain theorems
• generalized Nehari manifold

Under the Ambrosetti-Rabinowitz%26apos;s superquadraticy condition, or no Ambrosetti-Rabinowitz%26apos;s superquadracity condition, we present two results on the existence of infinitely many large energy homoclinic orbits when H is even in u. We apply the generalized (variant) fountain theorems established recently by the author and Colin. Under no Ambrosetti-Rabinowitz%26apos;s superquadracity condition, we also obtain the existence of a ground state homoclinic orbit by using the method of the generalized Nehari manifold for strongly indefinite functionals developed by Szulkin and Weth.

• 出版日期2014-9