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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Solution curves
for semilinear equations on a ball


Author: Philip Korman
Journal: Proc. Amer. Math. Soc. 125 (1997), 1997-2005
MSC (1991): Primary 35J60
DOI: https://doi.org/10.1090/S0002-9939-97-04119-1
MathSciNet review: 1423311
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Abstract: We show that the set of positive solutions of semilinear Dirichlet problem on a ball of radius $R$ in $R^n$

\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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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-97-04119-1
Keywords: Dirichlet problem on a ball, Crandall-Rabinowitz theorem
Received by editor(s): January 9, 1996
Communicated by: Jeffrey B. Rauch
Article copyright: © Copyright 1997 American Mathematical Society