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

2010/09/14 by Fokam, Jean Marcel
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1009.2801

Abstract

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

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