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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Radial Solutions to a Dirichlet Problem Involving Critical Exponents when $N=6$
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by Alfonso Castro and Alexandra Kurepa PDF
Trans. Amer. Math. Soc. 348 (1996), 781-798 Request permission

Abstract:

In this paper we show that, for each $\lambda > 0$, the set of radially symmetric solutions to the boundary value problem \[ \begin {aligned} -\Delta u(x) &= \lambda u(x) + u(x)\vert u(x)\vert , && x\in B := \{x\in R^6\colon \|x < 1\| \},\\ u(x) &= 0, && x\in \partial B, \end {aligned} \] is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.
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Additional Information
  • Alfonso Castro
  • Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203-5116
  • Email: acastro@unt.edu
  • Alexandra Kurepa
  • Affiliation: Department of Mathematics, North Carolina A&T State University, Greensboro, North Carolina 27411
  • Email: kurepaa@athena.ncat.edu
  • Received by editor(s): July 13, 1994
  • Received by editor(s) in revised form: February 7, 1995
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 781-798
  • MSC (1991): Primary 35J65, 34A10
  • DOI: https://doi.org/10.1090/S0002-9947-96-01476-6
  • MathSciNet review: 1321571