摘要：本文主要讨论了高阶kirchhoff方程的整体吸引子，对于低阶kirchhoff方程的整体吸引子，已有相当的研究.本文在低阶型kirchhoff方程研究的基础上，研究了一类广义非线性高阶kirchhoff型方程的整体吸引子.首先，在对高阶kirchhoff方程中的非线性项做出合理的假设下，得到方程的整体解和吸收集，然后由整体吸引子的判定定理(渐近紧性)，得到此类高阶kirchhoff方程的整体吸引子.
关键词：高阶Kirchhoff方程；整体解；吸收集；整体吸引子
中图分类号：O175
Global Attractor for a Class of Generalized Nonlinear nonlocal Higher-Order Kirchhoff Type Equations
LU Jingxin
(1Department of Information, Tourism and Culture College of Yunnan University,Lijiang,Yunnan 674199
2School of Mathematics and Statistics,Yunnan University,kunming 650500,yunnan,China)
Abstract：In this paper, we mainly discuss the global attractor of higher order Kirchhoff equation. For lower order Kirchhoff equation, the global attractor has been studied considerably. In this paper, the global attractors of a class of generalized nonlinear higher-order Kirchhoff equation are studied on the basis of the study of lower-order Kirchhoff equation. Firstly, under the reasonable assumption of the non-linear term in the higher-order Kirchhoff equation, the global solution and the absorbing set of the equation are obtained. Then, the global attractor of the higher-order Kirchhoff equation is obtained by the determination theorem of the global attractor (asymptotic compactness).
Key words：Higher-Order Kirchhoff equations；global solutions；absorbing set；global attractors
1 引言
本文研究下列非线性高阶Kirchhoff型方程的整体吸引子：
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