Higher order averaging theory for finding periodic solutions via Brouwer degree

被引：127

作者：

Llibre, Jaume ^{[1
]}

Novaes, Douglas D. ^{[1
,2
]}

Teixeira, Marco A. ^{[2
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

[2] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP, Brazil

来源：

NONLINEARITY | 2014年 / 27卷 / 03期

基金：

巴西圣保罗研究基金会;

关键词：

periodic solution; averaging method; non-smooth differential system; discontinuous differential system; Brouwer degree; LIMIT-CYCLES; LIENARD EQUATIONS; UNIQUENESS; ORBITS;

D O I：

10.1088/0951-7715/27/3/563

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we deal with nonlinear differential systems of the form x'(t) = Sigma(k)(i=0) epsilon(i) F(i()t,x) + epsilon(k+1) R(t,x,epsilon), where F-i : R x D -> R-n for i = 0, 1, ... , k, and R : R x D x (-epsilon 0, epsilon 0). R-n are continuous functions, and T - periodic in the first variable, D being an open subset of R-n, and epsilon a small parameter. For such differential systems, which do not need to be of class C-1, under convenient assumptions we extend the averaging theory for computing their periodic solutions to k-th order in epsilon. Some applications are also performed.

引用

页码：563 / 583

页数：21

共 27 条

[1]

[Anonymous], 1928, REV GENERALE LELECTR, DOI DOI 10.1016/J.JWEIA.2013.09.002

[2]

[Anonymous], 2007, Appl. Math. Sci

[3]

Bogoliubov N. N., 1945, SOME STAT METHODS MA

[4]

Bogoliubov N.N., 1934, The application of methods of nonlinear mechanics in the theory of stationary oscillations

[5]

Bowman F, 1958, Introduction to Bessel Function

[6] FIXED-POINT THEORY AND NON-LINEAR PROBLEMS [J].

BROWDER, FE .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 9 (01) :1-39

[7] Averaging methods for finding periodic orbits via Brouwer degree [J].

Buica, A ;

Llibre, J .

BULLETIN DES SCIENCES MATHEMATIQUES, 2004, 128 (01) :7-22

[8]

Conti R., 1998, MATHEMATICHE, V2, P207

[9]

Coppel WA., 1989, Dyn. Rep, V2, P61

[10] CUBIC LIENARD EQUATIONS WITH LINEAR DAMPING [J].

DUMORTIER, F ;

ROUSSEAU, C .

NONLINEARITY, 1990, 3 (04) :1015-1039

← 1 2 3 →