Massive Cantor families of periodic solutions of resonant Klein-Gordon equation on $\mathbb{S}^3$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909322868424704 |
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| author | Silimbani, Diego |
| author_facet | Silimbani, Diego |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Massive Cantor families of periodic solutions of resonant Klein-Gordon equation on $\mathbb{S}^3$ Silimbani, Diego Analysis of PDEs Mathematical Physics 37K58, 58E07, 35L05, 58J45, 83C10 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. |
| title | Massive Cantor families of periodic solutions of resonant Klein-Gordon equation on $\mathbb{S}^3$ |
| topic | Analysis of PDEs Mathematical Physics 37K58, 58E07, 35L05, 58J45, 83C10 |
| url | https://arxiv.org/abs/2409.14845 |