Multiplicity and regularity of large periodic solutions with rational frequency for a class of semilinear monotone wave equations

Details Multiplicity and regularity of large periodic solutions with rational frequency for a class of semilinear monotone wave equations Multiplicity and regularity of large periodic solutions with rational frequency for a class of semilinear monotone wave equations

2010-08-26

arxiv.org/abs/1008.4550v1

Mathematics

Analysis of PDEs

Scientific paper

We prove existence of infinitely many classical periodic solutions with periodic boundary conditions for a class of monotone semilinear wave equations. Our argument relies on some new estimates for the linear problem with periodic boundary conditions by combining Littewood-Paley techniques, the Hausdorff-Young theorem and a variational formulation due to Rabinowitz. We also develop a new approach to the regularity of distributional solutions by differentiating the equations and employing Gagliardo-Nirenberg estimates.

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