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Isolated singularities for elliptic equations with Hardy operator and source nonlinearity

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Huyuan Chen, Feng Zhou

Analysis of PDEs · Submitted 6 Jun 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim \end{equation} We classify the isolated singularities and obtain the existence, the stability of positive solutions of (\ref{0}).

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arXiv ID1706.01793 (version 2)
Pith IDYWVGKV3R, Pith's permanent record of this paper and its review
CitationFeng Zhou, Huyuan Chen. "Isolated singularities for elliptic equations with Hardy operator and source nonlinearity." arXiv:1706.01793 (2017). https://pith.science/paper/YWVGKV3R
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,087 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.05 · mentions code or data availability 0.01.

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In this paper, we concern the isolated singular solutions for semi-linear elliptic equations involving the Hardy-Leray potentials \begin{equation}\label{0} -\Delta u+\frac{\mu}{|x|^2} u=u^p\quad {\rm in}\quad \Omega\setminus\{0\},\qquad u=0\quad{\rm on}\quad \partial\Omega. \end{equation} We classify the isolated singularities and obtain the existence, the stability of positive solutions of (\ref{0}). Our results are based on the study of nonhomogeneous Hardy problem in a new distributional sense.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper, we concern the isolated singular solutions for semi-linear elliptic equations involving the Hardy-Leray potentials \begin{equation}\label{0} -\Delta u+\frac{\mu}{|x|^2} u=u^p\quad {\rm in}\quad \Omega\setminus\{0\},\qquad u=0\quad{\rm on}\quad \partial\Omega. background 0.71 0.40 0.06 asserted 0.68
s1 \end{equation} We classify the isolated singularities and obtain the existence, the stability of positive solutions of (\ref{0}). result 0.71 0.95 0.80 asserted 1.00
s2 Our results are based on the study of nonhomogeneous Hardy problem in a new distributional sense. method 0.90 0.72 0.05 asserted 1.00

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

In this paper, we concern the isolated singular solutions for semi-linear elliptic equations involving the Hardy-Leray potentials \begin{equation}\label{0} -\Delta u+\frac{\mu}{|x|^2} u=u^p\quad {\rm in}\quad \Omega\setminus\{0\},\qquad u=0\quad{\rm on}\quad \partial\Omega. \end{equation} We classify the isolated singularities and obtain the existence, the stability of positive solutions of (\ref{0}). Our results are based on the study of nonhomogeneous Hardy problem in a new distributional sense.

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