[2312.16368] On existence, uniqueness and radiality of normalized solutions to Schrödinger-Poisson equations with non-autonomous nonlinearity Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2312.16368 (math) This paper has been withdrawn by Chengcheng Wu [Submitted on 27 Dec 2023 ( v1 ), last revised 2 Aug 2026 (this version, v4)] Title: On existence, uniqueness and radiality of normalized solutions to Schrödinger-Poisson equations with non-autonomous nonlinearity Authors: Chengcheng Wu View a PDF of the paper titled On existence, uniqueness and radiality of normalized solutions to Schr\"{o}dinger-Poisson equations with non-autonomous nonlinearity, by Chengcheng Wu No PDF available, click to view other formats Abstract: We investigate the existence, uniqueness, and radial symmetry of normalized solutions to the Schrödinger Poisson equation with non-autonomous nonlinearity $f(x,u)$: \begin{equation} -\triangle u+(|x|^{-1}*|u|^2)u=f(x,u)+\lambda u, \nonumber \end{equation} subject to the constraint $\mathcal{S}_c=\{u\in H^1(\mathbb{R}^3)|\int_{\mathbb{R}^3}u^2=c>0 \}$. We consider three cases based on the behavior of $f(x,u)$: the $L^2$ supercritical case, the $L^2$ subcritical case with growth speed less than three power times, and the $L^2$ subcritical case with growth speed more than three power times. We establish the existence of solutions using three different methods depending on $f(x,u)$. Furthermore, we demonstrate the uniqueness and radial symmetry of normalized solutions using an implicit function framework when $c$ is small. Comments: There exists some errors Subjects: Analysis of PDEs (math.AP) Cite as: arXiv:2312.16368 [math.AP] (or arXiv:2312.16368v4 [math.AP] for this version) https://doi.org/10.48550/arXiv.2312.16368 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Chengcheng Wu [ view email ] [v1] Wed, 27 Dec 2023 01:05:17 UTC (27 KB) [v2] Thu, 4 Sep 2025 08:21:43 UTC (1 KB) (withdrawn) [v3] Fri, 24 Apr 2026 00:44:17 UTC (1 KB) (withdrawn) [v4] Sun, 2 Aug 2026 01:08:02 UTC (1 KB) (withdrawn) Full-text links: Access Paper: View a PDF of the paper titled On existence, uniqueness and radiality of normalized solutions to Schr\"{o}dinger-Poisson equations with non-autonomous nonlinearity, by Chengcheng Wu Withdrawn No license for this version due to withdrawn Current browse context: math.AP < prev | next > new | recent | 2023-12 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from