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Title: Periodic solutions of a weakly nonlinear hyperbolic equation in $E_2$ and $E_3$ (English)
Author: Vítek, Václav
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 19
Issue: 4
Year: 1974
Pages: 232-245
Summary lang: English
Summary lang: Czech
Category: math
Summary: For $n=2$ and 3 the existence and uniqueness of classical periodic solution of $\square_nu+2au_t+2(B,\nabla_nu)+cu=h(t,x)+\epsilon f(t,x,u,\epsilon)$ $(x=(x_1, x_2,\ldots,x_n))$ is proved assuming the periodicity of the right-hand side. ()
MSC: 35B10
MSC: 35B20
MSC: 35L60
idZBL: Zbl 0311.35004
idMR: MR0402292
Date available: 2008-05-20T17:59:12Z
Last updated: 2015-08-05
Stable URL:
Reference: [1] R. Courant D. Hilbert: Methoden der mathematischen Physik.Vol. 2, Berlin 1937.
Reference: [2] F. A. Ficken B. A. Fleishman: Initial value problems and time-periodic solutions for a nonlinear wave equation.Comm. pure appl. math. 10 (1957), 331 - 356. MR 0092080, 10.1002/cpa.3160100303
Reference: [3] J. Havlová: Periodic solutions of a nonlinear telegraph equation.Čas. pěst. mat. 90 (1965), 273-289. MR 0192180
Reference: [4] L. V. Kantorovič G. P. Akilov: Funkcionaľnyj analiz v normirovanych prostranstvach.Moskva 1959.
Reference: [5] G. N. Watson: A treatise on the theory of Bessel functions.2nd ed. Cambridge U.P. 1944. Zbl 0063.08184, MR 0010746


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