Proceedings of the American Mathematical Society

Author(s): Philip Korman
Journal: Proc. Amer. Math. Soc. 125 (1997), 1997-2005.
MSC (1991): Primary 35J60
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Abstract: We show that the set of positive solutions of semilinear Dirichlet problem on a ball of radius $R$

$\begin{displaymath}\Delta u+\lambda f(u)=0 \; \; \text {for} \; \; |x|<R, \; \; u=0 \; \; \text {on} \; \; |x|=R \end{displaymath}$

consists of smooth curves. Our results can be applied to compute the direction of bifurcation. We also give an easy proof of a uniqueness theorem due to Smoller and Wasserman (1984).

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 35J60

Philip Korman
Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025
Email: korman@ucbeh.san.uc.edu

DOI: 10.1090/S0002-9939-97-04119-1
PII: S 0002-9939(97)04119-1
Keywords: Dirichlet problem on a ball, Crandall-Rabinowitz theorem
Received by editor(s): January 9, 1996
Communicated by: Jeffrey B. Rauch
Copyright of article: Copyright 1997, American Mathematical Society

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