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Quasiperiodic solutions of completely resonant wave equations with quasiperiodic forced terms. (English) Zbl 1474.35483

Summary: This paper is concerned with the existence of quasiperiodic solutions with two frequencies of completely resonant, quasiperiodically forced nonlinear wave equations subject to periodic spatial boundary conditions. The solutions turn out to be, at the first order, the superposition of traveling waves, traveling in the opposite or the same directions. The proofs are based on the variational Lyapunov-Schmidt reduction and the linking theorem, while the bifurcation equations are solved by variational methods.

MSC:

35L71 Second-order semilinear hyperbolic equations
35B15 Almost and pseudo-almost periodic solutions to PDEs
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