Abstract

Solutions of functional differential equation of pointwise type (FDEPT) are in one-to-one correspondence with the traveling-wave type solutions for the canonically induced infinite-dimensional ordinary differential equation and vice versa. In particular, such infinite-dimensional ordinary differential equations are finite difference analogues of equations of mathematical physics. An important class of traveling-wave type solutions is made up of periodic and bounded traveling-wave type solutions. On the other hand, an important class of such systems is systems with strongly nonlinear potentials (polynomial potentials), for which periodic and bounded traveling wave solutions are studied. Such a problem is equivalent to the study of periodic and bounded solutions of the induced FDEPT to which the present work is devoted.

中文翻译：

---

具有强非线性右侧的点型泛函型微分方程的周期解和有界解的存在性

摘要

逐点型泛函微分方程（FDEPT）的解与经典诱导的无限维常微分方程的行波型解一一对应，反之亦然。特别地，这种无限维常微分方程是数学物理方程的有限差分类似物。一类重要的行波型解决方案由周期和有界行波型解决方案组成。另一方面，这类系统的重要一类是具有强非线性电势（多项式电势）的系统，对此系统研究了周期和有界行波解。这样的问题等同于研究诱导FDEPT的周期解和有界解，本研究致力于此问题。