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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Radial regular and rupture solutions for a PDE problem with gradient term and two parameters
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by Marius Ghergu and Yasuhito Miyamoto PDF
Proc. Amer. Math. Soc. 150 (2022), 1697-1709 Request permission


We investigate radial solutions for the problem \[ \begin {cases} \displaystyle -\Delta U=\frac {\lambda +\delta |\nabla U|^2}{1-U},\; U>0 & \text {in}\ B,\\ U=0 & \text {on}\ \partial B, \end {cases} \] where $B\subset \mathbb {R}^N$ $(N\geq 2)$ denotes the open unit ball and $\lambda , \delta >0$ are real numbers. Two classes of solutions are considered in this work: (i) regular solutions, which satisfy $0<U<1$ in $B$, and (ii) rupture solutions, which satisfy $U(0)=1$, and thus make the equation singular at the origin. Bifurcation with respect to parameter $\lambda >0$ is also discussed.
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Additional Information
  • Marius Ghergu
  • Affiliation: School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland; and Institute of Mathematics Simion Stoilow of the Romanian Academy, 21 Calea Grivitei St., 010702 Bucharest, Romania
  • MR Author ID: 700524
  • ORCID: 0000-0001-9104-5295
  • Email:
  • Yasuhito Miyamoto
  • Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
  • MR Author ID: 752875
  • ORCID: 0000-0002-7766-1849
  • Email:
  • Received by editor(s): June 30, 2020
  • Received by editor(s) in revised form: July 27, 2021
  • Published electronically: January 20, 2022
  • Additional Notes: The second author was supported by JSPS KAKENHI Grant Numbers 19H01797 and 19H05599.
  • Communicated by: Ryan Hynd
  • © Copyright 2022 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 150 (2022), 1697-1709
  • MSC (2020): Primary 34A12, 35B32; Secondary 35B40, 35J62
  • DOI:
  • MathSciNet review: 4375756