Annali di Matematica Pura ed Applicata (1923 -)

, Volume 198, Issue 6, pp 2183–2193 | Cite as

On the classification of solutions of cosmic strings equation

  • Weiwei Ao
  • Wen YangEmail author


In this paper, we prove some Liouville-type theorems for weak stable or finite Morse index solutions to the following equation:
$$\begin{aligned} \Delta u+e^u+|x|^\alpha e^{\beta u}=0\quad \mathrm {in}\quad \mathbb {R}^N, \end{aligned}$$
which arises from the study of selfgravitating cosmic strings for a massive W-boson model coupled with Einstein’s equation.

Mathematics Subject Classification

35J15 35J60 35J61 



The research of the first author is supported by NSFC Nos.11801421 and 11631011. The research of the second author is supported by NSFC Nos.11801550 and 11871470.


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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanPeople’s Republic of China
  2. 2.Wuhan Institute of Physics and MathematicsChinese Academy of SciencesWuhanPeople’s Republic of China

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