Positive periodic solution to indefinite singular Lienard equation

被引:5
作者
Xin, Yun [1 ]
Cheng, Zhibo [2 ,3 ]
机构
[1] Henan Polytech Univ, Coll Comp Sci & Technol, Jiaozuo 454000, Henan, Peoples R China
[2] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China
[3] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Henan, Peoples R China
基金
中国博士后科学基金; 中国国家自然科学基金;
关键词
Positive periodic solution; Indefinite singularity; Lienard equation; DIFFERENTIAL-EQUATIONS; SUBHARMONIC SOLUTIONS; DUFFING EQUATION; MULTIPLICITY;
D O I
10.1007/s11117-018-0637-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we investigate the existence of a positive periodic solution for the following Lienard equation with a indefinite singularity x ''+f(x)x '+b(t)x=p(t), is a T-periodic sign-changing function. The novelty of the present article is that for the first time we show that a indefinite singularity enables the achievement of a new existence criterion of positive periodic solutions through a application of a topological degree theorem by Mawhin. Recent results in the literature are generalized and significantly improved, and we give the existence interval of a positive periodic solution of this equation. At last, an example is given to show applications of the theorems.
引用
收藏
页码:779 / 787
页数:9
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