Title:

Small timeperiodic solutions to a nonlinear equation of a vibrating string (English) 
Author:

Feireisl, Eduard 
Language:

English 
Journal:

Aplikace matematiky 
ISSN:

03736725 
Volume:

32 
Issue:

6 
Year:

1987 
Pages:

480490 
Summary lang:

English 
Summary lang:

Russian 
Summary lang:

Czech 
. 
Category:

math 
. 
Summary:

In this paper, the system consisting of two nonlinear equations is studied. The former is hyperbolic with a dissipative term and the latter is elliptic. In a special case, the system reduces to the approximate model for the damped transversal vibrations of a string proposed by G. F. Carrier and R. Narasimha. Taking advantage of accelerated convergence methods, the existence of at least one timeperiodic solution is stated on condition that the righthand side of the system is sufficiently small. (English) 
Keyword:

nonlinear string equation 
Keyword:

accelerated convergence 
Keyword:

existence 
Keyword:

periodic 
Keyword:

Dirichlet boundary conditions 
Keyword:

vibrations 
Keyword:

damped extensive string 
Keyword:

timeperiodic solution 
MSC:

35B10 
MSC:

35L70 
MSC:

58C15 
MSC:

73K03 
idZBL:

Zbl 0653.35063 
idMR:

MR0916063 
DOI:

10.21136/AM.1987.104278 
. 
Date available:

20080520T18:33:33Z 
Last updated:

20200728 
Stable URL:

http://hdl.handle.net/10338.dmlcz/104278 
. 
Reference:

[1] R. W. Dickey: Infinite systems of nonlinear oscillation equations with Linear Damping.Siam J. Appl. Math. 19 (1970), pp. 208214. Zbl 0233.34014, MR 0265654, 10.1137/0119019 
Reference:

[2] S. Klainerman: Global existence for nonlinear wave equations.Comm. Pure Appl. Math. 33 (1980), pp. 43101. Zbl 0405.35056, MR 0544044, 10.1002/cpa.3160330104 
Reference:

[3] P. Krejčí: Hard Implicit Function Theorem and Small periodic solutions to partial differential equations.Comment. Math. Univ. Carolinae 25 (1984), pp. 519536. MR 0775567 
Reference:

[4] J. Moser: A rapidlyconvergent iteration method and nonlinear differential equations.Ann. Scuola Norm. Sup. Pisa 203 (1966), pp. 265315, 499535. 
Reference:

[5] O. Vejvoda, et al.: Partial differential equations: Timeperiodic Solutions.Martinus Nijhoff Publ., 1982. Zbl 0501.35001 
. 