Multiplicity and regularity of periodic solutions for a class of degenerate semilinear wave equations

2010/12/24 by Fokam, Jean Marcel
#35A15 35Jxx 35B45 35L05 35B10 42B35 34C25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1012.5428

Abstract

We prove the existence of infinitely many classical periodic solutions for a class of degenerate semilinear wave equations: u_tt-u_xx+|u|^s-1u=f(x,t), for all s>1. In particular we prove the existence of infinitely many classical solutions for the case s=3 posed by Brézis in \citeBrezisBAMS. The proof relies on a new upper a priori estimates for minimax values of, a pertubed from symmetry, strongly indefinite functional,depending on a small parameter.

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