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

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.