## Solution curves for semilinear equations on a ball

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- by Philip Korman
- Proc. Amer. Math. Soc.
**125**(1997), 1997-2005 - DOI: https://doi.org/10.1090/S0002-9939-97-04119-1
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## Abstract:

We show that the set of positive solutions of semilinear Dirichlet problem on a ball of radius $R$ in $R^n$ \[ \Delta u+\lambda f(u)=0 \; \; \text {for} \; \; |x|<R, \; \; u=0 \; \; \text {on} \; \; |x|=R \] 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).## References

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## Bibliographic Information

**Philip Korman**- Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025
- MR Author ID: 200737
- Email: korman@ucbeh.san.uc.edu
- Received by editor(s): January 9, 1996
- Communicated by: Jeffrey B. Rauch
- © Copyright 1997 American Mathematical Society
- 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