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Non-radial solutions to a bi-harmonic equation with negative exponent

  • Ali HyderEmail author
  • Juncheng Wei
Article
  • 94 Downloads

Abstract

We prove the existence of smooth non-radial entire solution to
$$\begin{aligned} \Delta ^2 u+u^{-q}=0\quad \text {in }\mathbb {R}^3,\quad u>0, \end{aligned}$$
for \(q>1\). This answers an open question raised by McKenna and Reichel (Electron J Differ Equ 37:1–3, 2003).

Mathematics Subject Classification

35J61 35B40 53A30 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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