带时滞的Laplacian型方程周期解的存在唯一性  

Existence and Uniqueness of Periodic Solutions for a Laplacian-like Equation with a Deviating Argument

作　　者：李志艳[1,2] 严树林[3] 张斌武[1] 葛渭高[4] 

机构地区：[1]河海大学常州校区数理部,江苏常州213022 [2]河海大学理学院,江苏常州210098 [3]常州工程职业技术学院基础部,江苏常州213164 [4]北京理工大学数学系,北京100081

出　　处：《数学的实践与认识》2016年第7期276-281,共6页Mathematics in Practice and Theory

基　　金：中央高校基本科研基金(2014B11414)

摘　　要：利用拓扑度理论和Mawhin's连续定理,研究了一类带有偏差变元的Laplacian型常微分方程的周期解,使用不等式和分析技巧,建立方程解的存在及唯一性条件.有意思的是,与已有文献相比,用来估计先验界的方法是新的,最后,给出了一个实例,验证了所得结论.By means of topological theory and Mawhin＇ s continuation theorem, a kind of Laplacian-like li e nard differential equation with a deviating argument is studied. The authors establish some criteria to guarantee the existence and uniqueness of periodic solutions using some inequalities and mathematical analysis techniques. It is meaningful that, compared with the corresponding ones in the know literature, the approaches uesed to estimate a prior bounds of periodic solutions are essentially new. Moreover, we give an example to illustrate our main results.

关 键 词：Laplacian型算子 Mawhin’s连续定理 周期解 LIENARD方程 

分 类 号：O175[理学—数学]