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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.12962 |
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| _version_ | 1866911061301526528 |
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| author | Cannone, Alessandro Cingolani, Silvia Mederski, Jarosław |
| author_facet | Cannone, Alessandro Cingolani, Silvia Mederski, Jarosław |
| contents | In this paper, we present a result on the existence of ground state solutions for the polyharmonic nonlinear equation $(-Δ)^m u=g(u)$, assuming that $g$ has a general subcritical growth at infinity, inspired by Berestycki and Lions \cite{BerestyckiLions}. In comparison with the biharmonic case studied in \cite{Med-Siem}, the presence of a higher-order operator gives rise to several analytical challenges, which are overcome in the present work. Furthermore, we establish a new polyharmonic logarithmic Sobolev inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12962 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polyharmonic Nonlinear Scalar Field Equations Cannone, Alessandro Cingolani, Silvia Mederski, Jarosław Analysis of PDEs 35J91, 35J20 In this paper, we present a result on the existence of ground state solutions for the polyharmonic nonlinear equation $(-Δ)^m u=g(u)$, assuming that $g$ has a general subcritical growth at infinity, inspired by Berestycki and Lions \cite{BerestyckiLions}. In comparison with the biharmonic case studied in \cite{Med-Siem}, the presence of a higher-order operator gives rise to several analytical challenges, which are overcome in the present work. Furthermore, we establish a new polyharmonic logarithmic Sobolev inequality. |
| title | Polyharmonic Nonlinear Scalar Field Equations |
| topic | Analysis of PDEs 35J91, 35J20 |
| url | https://arxiv.org/abs/2507.12962 |