Geodesic
Periodic Solutions of a Quasilinear Wave Equation
Matematičeskie zametki, Tome 85 (2009) no. 1, pp. 36-53

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We study the properties of wave operators satisfying the periodicity condition with respect to time and homogeneous boundary conditions of the third kind and of Dirichlet type. We prove the existence of a nontrivial periodic (in time) $\sin$-Gordon solution with homogeneous boundary conditions of the third kind and of Dirichlet type. We obtain theorems on the existence of periodic solutions of a quasilinear wave equation with variable (in $x$) coefficients and a boundary condition of the third kind.
Keywords: quasilinear wave equation, boundary condition of the third kind, Dirichlet boundary condition, Sobolev space.
Mots-clés : $\sin$-Gordon solution, Sturm–Liouville problem 
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     author = {V. A. Kondrat'ev and I. A. Rudakov},
     title = {Periodic {Solutions} of a {Quasilinear} {Wave} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {36--53},
     publisher = {mathdoc},
     volume = {85},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a3/}
}
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V. A. Kondrat'ev; I. A. Rudakov. Periodic Solutions of a Quasilinear Wave Equation. Matematičeskie zametki, Tome 85 (2009) no. 1, pp. 36-53. http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a3/