关于《Existence and Multiplicity of Traveling Waves in a lattice Dynamical System》的注记

Notes on《Existence and Multiplicity of Traveling Waves in a Lattice Dynamical System》

文章《Existence and Multiplicity of Traveling Waves in a lattice Dynamical System》利用单调迭代格式和上下解方法研究了一个格动力系统小于临界波速的行波解的存在性,而当波速等于临界波速时不易通过构造上下解来证明其行波解的存在性,该文利用极限方法证明了原格动力系统的具有临界波速的行波解。

The paper 《 Existence and Multiplicity of Traveling Waves in a Lattice Dynamical System》deals with the existence of traveling wave fronts in a lattice dynamical system when velocity less than critical velocity. The approach used in the paper is the upper - lower solution technique and the monotonic iteration methods. But when velocity equals to critical velocity, it is not easy to construct the upper - lower solution to show the existence of such a solution. This paper proves the existence of traveling wave fronts with critical velocity in the primary lattice dynamical system. The existence of such solutions is proved by way of the technique of limit.