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arXiv · 2409.14845

Massive Cantor families of periodic solutions of resonant Klein-Gordon equation on $\mathbb{S}^3$

Diego Silimbani
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Abstract

We prove existence and multiplicity of Cantor families of small amplitude analytic in time periodic solutions of the completely resonant cubic nonlinear Klein-Gordon equation on $\mathbb{S}^3$ for an asymptotically full measure set of frequencies close to 1. The solutions are constructed by a Lyapunov-Schmidt decomposition and a Nash-Moser iterative scheme. We first find non-degenerate solutions of the Kernel equation. Then we solve the Range equation with a Nash-Moser iterative scheme to overcome small divisors problems.

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Diego Silimbani. 2024-09-23. Massive Cantor families of periodic solutions of resonant Klein-Gordon equation on $\mathbb{S}^3$. https://arxiv.org/abs/2409.14845

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