叠合度的缺方向性与边值共振问题的非平凡解

Lack of Direction Property of the Coincidence Degree and Applications

中文关键词:  叠合度  缺方向性  非平凡解  边值问题

英文关键词:coincidence degree I the lack of property  nontrivial solution  boundary valueproblem.

中文摘要:

      本文在无任何附加条件的情况下证明了叠合度也具有Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ度的缺方向性质，完全解决了前人工作中的遗留问题．作为这一结果的应用，证明了一类ｍ－点边值问题和Ｄｕｆｆｉｎｇ方程周期边值问题非平凡解的存在性结果．

英文摘要:

      In this paper, the lack of direction property of the coincidence degree, which wasproved partially in [3], is proved completely without any additional condition. As applications, the existence of nontrivial solutions of a class of m-point boundary value problem atresonance and periodic boundary value problem for Duffing equation is dicussed.