Isolated singularities for elliptic equations with Hardy operator and source nonlinearity

Huyuan Chen; Feng Zhou

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arXiv · 1706.01793

Isolated singularities for elliptic equations with Hardy operator and source nonlinearity

Huyuan Chen·Feng Zhou

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Abstract

In this paper, we concern the isolated singular solutions for semi-linear elliptic equations involving the Hardy-Leray potentials \begin{equation}\label{0} -Δu+\fracμ{|x|^2} u=u^p\quad {\rm in}\quad Ω\setminus\{0\},\qquad u=0\quad{\rm on}\quad \partialΩ. \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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Huyuan Chen, Feng Zhou. 2017-06-25. Isolated singularities for elliptic equations with Hardy operator and source nonlinearity. https://arxiv.org/abs/1706.01793

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