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

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

2010-12-24

arxiv.org/abs/1012.5428v4

Mathematics

Analysis of PDEs

Previous version had a computationl error in section 1 and a mistake in section 2

Scientific paper

We prove the existence of infinitely many classical periodic solutions for a class of degenerate semilinear wave equations: \[ u_{tt}-u_{xx}+|u|^{s-1}u=f(x,t), \] for all $s>1$. In particular we prove the existence of infinitely many classical solutions for the case $s=3$ posed by Br\'ezis in \cite{BrezisBAMS}. 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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