Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Radially symmetric solutions to a Dirichlet problem involving critical exponents


Authors: Alfonso Castro and Alexandra Kurepa
Journal: Trans. Amer. Math. Soc. 343 (1994), 907-926
MSC: Primary 35B05; Secondary 35J65
MathSciNet review: 1207581
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we answer, for $ N = 3,4$, the question raised in [1] on the number of radially symmetric solutions to the boundary value problem $ - \Delta u(x) = \lambda u(x) + u(x)\vert u(x){\vert^{4/(N - 2)}}$, $ x \in B: = \{ x \in {R^N}:\left\Vert x \right\Vert < 1\} $, $ u(x) = 0$, $ x \in \partial B$, where $ \Delta $ is the Laplacean operator and $ \lambda > 0$. Indeed, we prove that if $ N = 3,4$, then for any $ \lambda > 0$ this problem has only finitely many radial solutions. For $ N = 3,4,5$ we show that, for each $ \lambda > 0$, the set of radially symmetric solutions is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35B05, 35J65

Retrieve articles in all journals with MSC: 35B05, 35J65


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1207581-0
PII: S 0002-9947(1994)1207581-0
Keywords: Critical exponent, radially symmetric solutions, Dirichlet problem, nodal curves, bifurcation
Article copyright: © Copyright 1994 American Mathematical Society