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Vítek, Václav
Periodic solutions of a weakly nonlinear hyperbolic equation in $E_2$ and $E_3$. (English). Aplikace matematiky, vol. 19 (1974), issue 4, pp. 232-245
MSC: 35B10, 35B20, 35L60 | MR 0402292 | Zbl 0311.35004 | DOI: 10.21136/AM.1974.103537
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.
References:
[1] R. Courant D. Hilbert: Methoden der mathematischen Physik. Vol. 2, Berlin 1937.
[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. DOI 10.1002/cpa.3160100303 | MR 0092080
[3] J. Havlová: Periodic solutions of a nonlinear telegraph equation. Čas. pěst. mat. 90 (1965), 273-289. MR 0192180
[4] L. V. Kantorovič G. P. Akilov: Funkcionaľnyj analiz v normirovanych prostranstvach. Moskva 1959.
[5] G. N. Watson: A treatise on the theory of Bessel functions. 2nd ed. Cambridge U.P. 1944. MR 0010746 | Zbl 0063.08184
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