Time-periodic solutions of completely resonant Klein–Gordon equations on
Massimiliano Berti
International School for Advanced Studies (SISSA), Trieste, ItalyBeatrice Langella
International School for Advanced Studies (SISSA), Trieste, ItalyDiego Silimbani
International School for Advanced Studies (SISSA), Trieste, Italy
Abstract
We prove existence and multiplicity of Cantor families of small-amplitude time-periodic solutions of completely resonant Klein–Gordon equations on the sphere with quadratic, cubic, and quintic nonlinearity, regarded as toy models in general relativity. The solutions are obtained by a variational Lyapunov–Schmidt decomposition, which reduces the problem to the search of mountain pass critical points of a restricted Euler–Lagrange action functional. Compactness properties of its gradient are obtained by Strichartz-type estimates for the solutions of the linear Klein–Gordon equation on .
Cite this article
Massimiliano Berti, Beatrice Langella, Diego Silimbani, Time-periodic solutions of completely resonant Klein–Gordon equations on . Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024), published online first
DOI 10.4171/AIHPC/125