The existence and local uniqueness of the eigenfunctions of the non-linear operator $ Δ_H u^{n}$ in the hyperbolic Poincaré half-plane
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910098349096960 |
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| author | Maltese, F. |
| author_facet | Maltese, F. |
| contents | In this article we find locally an eigenfunctions for a particular nonlinear hyperbolic differential operator $Δ_H u^{n}$, where $Δ_H$ is the hyperbolic Laplacian in the half-plane of Poincairé. We have proved that these eigenfunctions are an analytic and non-exact whose coefficients satisfy a specific algebraic recursive rule. The existence of these eigenfunctions allows us to find non-exact solutions respecting the spatial coordinate of nonlinear diffusive PDEs on the Poincairé half-plane, which could describe a possible one-dimensional physical model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The existence and local uniqueness of the eigenfunctions of the non-linear operator $ Δ_H u^{n}$ in the hyperbolic Poincaré half-plane Maltese, F. Analysis of PDEs In this article we find locally an eigenfunctions for a particular nonlinear hyperbolic differential operator $Δ_H u^{n}$, where $Δ_H$ is the hyperbolic Laplacian in the half-plane of Poincairé. We have proved that these eigenfunctions are an analytic and non-exact whose coefficients satisfy a specific algebraic recursive rule. The existence of these eigenfunctions allows us to find non-exact solutions respecting the spatial coordinate of nonlinear diffusive PDEs on the Poincairé half-plane, which could describe a possible one-dimensional physical model. |
| title | The existence and local uniqueness of the eigenfunctions of the non-linear operator $ Δ_H u^{n}$ in the hyperbolic Poincaré half-plane |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.16168 |