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Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions. (English) Zbl 1186.35113
The authors prove the existence of Cantor families of periodic solutions to semilinear wave equation in higher spatial dimensions with periodic boundary conditions in forced and autonomous case. The proofs are based on a differentiable Nash-Moser iteration scheme. The key point of the iterative process lies in a priori bounds for the divergence of the high Sobolev norms of the approximate solutions.

MSC:
35L71 Second-order semilinear hyperbolic equations
35B10 Periodic solutions to PDEs
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