2m阶差分方程边值问题解的存在性

Existence of solutions to the boundary value problems of a 2mth-order difference equation

讨论一类2m阶非线性差分方程边值问题.通过建立相应的变分框架,将边值问题的解转换为对应的非线性泛函的临界点.利用环绕定理,获得变分泛函临界点的存在性,进而得到所求边值问题解的存在性.最后给出例子说明本文的结论.

Existence of solutions to the boundary value problems of a 2mth-order difference equation is considered in this paper. By establishing the corresponding variational structure, we transform the problem of the existence of solutions to the boundary value problems into the existence of the critical points for the corresponding variational functional. By using Linking Theorem, we obtain the existence of the critical points of the variational functional, and the existence of solutions of the boundary value problems is achieved as well. An illustrative example is presented at length to illustrate our conclusion.