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Transactions of the American Mathematical Society

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Radial Solutions to a Dirichlet Problem Involving Critical Exponents when $N = 6$


Authors: Alfonso Castro and Alexandra Kurepa
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
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we show that, for each $\lambda > 0$, the set of radially symmetric solutions to the boundary value problem

\begin{equation*}\begin{split} -\Delta u(x) & = % \lambda u(x) + u(x)\vert u(x)\vert,\quad x\in B := \{x\in R^6\colon\Vert x\Vert < 1\},\\ u(x) & = % 0, \quad x\in\partial B, \end{split} \end{equation*}

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

DOI: https://doi.org/10.1090/S0002-9947-96-01476-6
Keywords: Critical exponent, radially symmetric solutions, Dirichlet problem, nodal curves, bifurcation
Received by editor(s): July 13, 1994
Received by editor(s) in revised form: February 7, 1995
Article copyright: © Copyright 1996 American Mathematical Society

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