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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
DOI: https://doi.org/10.1090/S0002-9947-96-01476-6
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 \[ \begin {aligned} -\Delta u(x) &= \lambda u(x) + u(x)\vert u(x)\vert , && x\in B := \{x\in R^6\colon \|x < 1\| \},\\ u(x) &= 0, && x\in \partial B, \end {aligned} \] 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

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