Existence and uniqueness of periodic solutions for a kind of Liénard equation with multiple deviating arguments

被引：3

作者：

Hou X. ^{[1
]}

Wu Z. ^{[2
]}

机构：

[1] Hunan Industry Polytechnic, Changsha

[2] Yueyang Vocational Technical College, Yueyang

来源：

Journal of Applied Mathematics and Computing | 2012年 / 38卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

Coincidence degree; Liénard equation; Multiple deviating arguments; Periodic solution;

D O I：

10.1007/s12190-010-0472-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a kind of Liénard equation with multiple deviating arguments of the form x''(t)+f(x(t))x'(t)+ ∑ k=1 ngk(t,x(t-τ k(t)))=p(t) is considered. By using coincidence degree theory, some criteria are obtained to guarantee the existence and uniqueness of periodic solutions of this equation. The obtained results are also valid and new for the problem discussed in the previous literature. © 2011 Korean Society for Computational and Applied Mathematics.

引用

页码：181 / 193

页数：12

共 10 条

[1]

Gaines R.E., Mawhin J., Coincide Degree and Nonlinear Differential Equations, Lecture Notes in Mathematics, 568, (1977)

[2]

Huang X., Xiang Z., On existence of 2π-periodic solutions for delay Duffing equation x+g(t,x(t-τ(t))=p(t)), Chin. Sci. Bull., 39, pp. 201-203, (1994)

[3]

Lu S., Ge W., Periodic solutions for a kind of second order differential equation with multiple deviating argument, Appl. Math. Comput., 146, pp. 195-209, (2003)

[4]

Lu S., Ge W., Periodic solutions for a kind of Liéneard equations with deviating arguments, J. Math. Anal. Appl., 249, pp. 231-243, (2004)

[5]

Lu S., Ge W., Sufficient conditions for the existence of periodic solutions to some second order differential equations with a deviating argument, J. Math. Anal. Appl., 308, pp. 393-419, (2005)

[6]

Mawhin J., Periodic solution of some vector retarded functional differential equations, J. Math. Anal. Appl., 45, pp. 588-603, (1974)

[7]

Liu B.W., Existence and uniqueness of periodic solutions for a kind of Liéneard-type equations with a deviating argument, J. Syst. Sci. Math. Sci., 29, pp. 360-366, (2009)

[8]

Zhou Q., Long F., Existence and uniqueness of periodic solutions for a kind of Liéneard equation with two deviating arguments, J. Comput. Appl. Math., 206, pp. 1127-1136, (2007)

[9]

Hardy G.H., Littlewood J.E., Polua G., Inequalities, (1964)

[10]

Sirma A., Tunc C., Ozlem S., Existence and uniqueness of periodic solutions for a kind of Rayleigh equation with finitely many deviating arguments, Nonlinear Anal., 73, 2, pp. 358-366, (2010)

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