一类弱二次Hamilton系统的同宿解的多重性结果  

Multiplicity Result for Homoclinic Solutions to A Class of Subquadratic Hamiltonian Systems

作　　者：孙昭洪[1] 张玮[2] 贺铁山[1] 高川翔[1] 

机构地区：[1]仲恺农业工程学院计算科学学院,广州510225 [2]玉溪师范学院理学院,云南玉溪653100

出　　处：《数学物理学报（A辑）》2015年第2期364-372,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11401111);广东省教育科研十二五规划项目(2011TJK468)资助

摘　　要：考虑二阶非自治弱二次Hamilton系统同宿解的多重性.一般考虑的势函数关于u在无穷远点处的下界函数是一个正常数.而当该系数换为一个正函数而非常数时,情况就会相当不同.该文中讨论了这一问题,将此系数推广到下确界可以是0的一个有关t的正函数.因此该文的结果是对近期一些结果的有意义的改进.In the present paper we consider the multiplicity of homoclinic solutions for the second order non-autonomous subquadratic Hamiltonian system. In this case, the lower bounded coefficient of the potential function about u near infinity was required to be a positive constant in the literature. However, if the coefficient is a positive function but not a constant, the situation is quite different. In this paper we solved this question. We extent the coefficient to a positive function of t which minimum may be zero. Hence the result in this work is a significant improvement of the results in recent literature.

关 键 词：下界函数 弱二次势函数 多重性 同宿解 

分 类 号：O211.4[理学—概率论与数理统计]