一类具有偏差变元的p-Laplacian Liénard型方程在吸引奇性条件下周期解的存在性  

Periodic Solution for p-Laplacian Liénard Equation with Attractive Singularity and Time-Dependent Deviating Argument

作　　者：程志波[1,2] 毕中华 姚绍文 Zhibo Cheng;Zhonghua Bi;Shaowen Yao(School of Mathematics and Information Science, Henan Polytechnic University, Henan Jiaozuo 454003;Department of Mathematics, Sichuan University, Chengdu 610064)

机构地区：[1]河南理工大学数学与信息科学学院,河南焦作454003 [2]四川大学数学学院,成都610064

出　　处：《数学物理学报（A辑）》2019年第2期277-285,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11501170;71601072);中国博士后基金(2016M590886);河南省高校基本科研业务费专项资金(NSFRF170302);河南理工大学博士基金(B2013-055)~~

摘　　要：该文考虑了一类具有偏差变元的奇性P-Laplacian Lienard型方程(φ_p(x'(t))'+f(x(t))x'(t)+g(t, x(t-σ(t)))=e(t)其中g(x)在原点处具有吸引奇性.通过应用Manasevich-Mawhin连续定理和一些分析方法,证明了这个方程周期解的存在性.In this paper, we consider a kind of pp-Laplacian singular Liénard equation with time-dependent deviating argument (φp(x′(t)))′+f(x(t))x′(t)+g(t,x(t-σ(t)))=e(t), where gg has a attractive singularity at x=0. By applications of Manásevich-Mawhin continuation theorem and some analysis skills, sufficient conditions for the existence of periodic solution is established.

关 键 词：LIÉNARD型方程 周期解 吸引奇性 P-LAPLACIAN 偏差变元 

分 类 号：O175.12[理学—数学]