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Transactions of the American Mathematical Society

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



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
MathSciNet review: 1321571
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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

Alexandra Kurepa
Affiliation: Department of Mathematics, North Carolina A&T State University, Greensboro, North Carolina 27411

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