具有周期系数的Kirchhoff-型差分方程同宿解的存在性  

Homoclinic Solutions for the Kirchhoff-type Difference Equations with Periodic Coefficients

作　　者：王振国 丁廉业 WANG Zhenguo;DING Lianye(Department of Mathematics,Taiyuan University,Taiyuan 030032;School of Mathematics and Statistics,Huanghuai University,Zhumadian 463000)

机构地区：[1]太原学院数学系,太原030032 [2]黄淮学院数学与统计学院,驻马店463000

出　　处：《工程数学学报》2024年第5期973-979,共7页Chinese Journal of Engineering Mathematics

基　　金：河南省自然科学基金(232300420127);太原学院一般科研项目(23TYYB04).

摘　　要：运用临界点理论研究一类具有周期系数的Kirchhoff-型差分方程同宿解问题。首先,构造了差分方程所对应的能量泛函。在文中的假设条件下,保证了能量泛函具有山路几何结构,从而得到了一个Palais-Smale序列。然后,利用一个可变号的全局性条件证明了该Palais-Smale序列的有界性。进一步,借助于l^(2)空间的紧支撑子集的性质和系数的周期性得到了该差分方程的一个非平凡同宿解。最后,给出两个例子说明了主要结论的正确性。By means of critical point theory,we investigate homoclinic solution problems for the Kirchhoff-type difference equations with periodic coefficients.First,we verify that the graph of the energy functional satisfies the mountain pass geometrical properties.Such mountain pass geometry produces a Palais-Smale sequence.Second,we exploit one global property condition to guarantee that this Palais-Smale sequence is bounded.Further,by using the subset of l^(2)consisting of functions with compact support and periodicity of coefficients,we obtain the existence of one nontrivial homoclinic solution for the Kirchhoff-type difference equations with periodic coefficients.Finally,two examples are given to illustrate our main results.

关 键 词：Kirchhoff-型差分方程 同宿解 Palais-Smale序列 山路引理 

分 类 号：O175.8[理学—数学]