Abstract

In this paper, we aim to understand the characteristics of dynamical behaviour for a higher order Kirchhoff type systems with logarithmic nonlinearities. Based on the potential well method, the main ingredient of this study is to construct several conditions for initial data leading to the solution global existence in case of E (0) < d. On the other hand, we proved that if the solution lies in a smaller set compared with the stable set, we can estimate the decay rate of energy.

中文翻译：

---

具有对数非线性的高阶Kirchhoff型系统解的整体存在和衰减

摘要

在本文中，我们旨在了解具有对数非线性的高阶Kirchho ff型系统动力学行为的特征。基于势阱方法，本研究的主要内容是为E（0）<d情况下导致整体解存在的初始数据构建几个条件。另一方面，我们证明了，如果与稳定集相比解在较小的集合中，则可以估计能量的衰减率。