二阶哈密尔顿系统同宿解的多重性

Multiplicity of Homoclinic Solutions for Second Order Hamiltonian Systems

研究了一类二阶哈密尔顿系统在超二次条件下的同宿解的多重性问题.传统的方法是利用山路引理,寻找鞍点型临界点来解决同宿解的存在性.利用喷泉定理,推广了原有的结论,证明了在超二次条件下同宿解的多重性问题.

The multiplicity of homoclinic solutions for a class of second order Hamiltonian systems under the superquadratic condition is studied in this paper.The traditional method is to use the mountain pass lemma to find the critical point of saddle point type so as to solve the existence of homoclinic solutions.Using the Fountain theorem,our results extend some previously known results and prove the multiplicity of homoclinic solutions under the superquadratic condition.