The study of existence and multiplicity of time-periodic solutions for semilinear Klein-Gordon equation has recently been proposed as a toy model to understand stability properties of Anti-de Sitter spacetime under certain perturbation, a question which is of great interest in general relativity.
I will present a result on existence and multiplicity of Cantor families of small amplitude, analytic in time and periodic solutions for the completely resonant cubic nonlinear Klein-Gordon equation on S3 for an asymptotically full measure set of frequencies. The solutions are constructed by a Lyapunov- Schmidt decomposition and a Nash-Moser iterative scheme. We first find non-degenerate solutions of the resonant system, then, in view of small divisors problem, we solve the Range equation by a Nash-Moser iteration.
Diego Silimbani (Italy): Massive Cantor families of periodic solutions of resonant Klein-Gordon equation on S3
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