Geodesic
Existence of a countable set of periodic solutions of the problem of forced oscillations for a weakly nonlinear wave equation
Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 543-556 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the strip $0 of the plane of the points $t$, $x$ the following boundary value problem is considered: \begin{gather*} u_{tt}-u_{xx}=\pm|u|^{p-2}u+h(t,x)\quad(0<x<\pi),\qquad u(t,0)=u(t,\pi)=0, \\ u(t+2\pi,x)=u(t,x). \end{gather*} It is proved that for any $p>2$ and for an arbitrary $2\pi$-periodic function $h$ which is locally integrable with power $p(p-1)^{-1}$ this problem has a countable set of geometrically distinct generalized solutions. Bibliography: 15 titles. 
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     author = {P. I. Plotnikov},
     title = {Existence of a~countable set of periodic solutions of the problem of forced oscillations for a~weakly nonlinear wave equation},
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P. I. Plotnikov. Existence of a countable set of periodic solutions of the problem of forced oscillations for a weakly nonlinear wave equation. Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 543-556. http://geodesic.mathdoc.fr/item/SM_1989_64_2_a16/

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