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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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Exact multiplicity for some nonlinear elliptic equations in balls
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by Juncheng Wei PDF
Proc. Amer. Math. Soc. 125 (1997), 3235-3242 Request permission

Abstract:

We present the exact multiplicity results for some nonlinear elliptic equations in balls of radius $R$. We prove that there is a critical value $R_{0}$ such that, for $R < R_{0}$, the equation has no solution; when $R=R_{0}$, it has exactly one solution; when $R > R_{0}$, it has exactly two solutions. Our main tool is the bifurcation theorem due to Crandall and Rabinowitz.
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Additional Information
  • Juncheng Wei
  • Affiliation: Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong
  • MR Author ID: 339847
  • ORCID: 0000-0001-5262-477X
  • Email: wei@math.cuhk.edu.hk
  • Received by editor(s): December 15, 1995
  • Communicated by: Jeffrey Rauch
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3235-3242
  • MSC (1991): Primary 35B40, 35B45; Secondary 35J40
  • DOI: https://doi.org/10.1090/S0002-9939-97-04211-1
  • MathSciNet review: 1443172