## Exact multiplicity for some nonlinear elliptic equations in balls

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- by Juncheng Wei
- Proc. Amer. Math. Soc.
**125**(1997), 3235-3242 - DOI: https://doi.org/10.1090/S0002-9939-97-04211-1
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## Abstract:

We present the exact multiplicity results for some nonlinear elliptic equations in balls of radius $R$. We prove that there is a critical value $R_{0}$ such that, for $R < R_{0}$, the equation has no solution; when $R=R_{0}$, it has exactly one solution; when $R > R_{0}$, it has exactly two solutions. Our main tool is the bifurcation theorem due to Crandall and Rabinowitz.## References

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## Bibliographic Information

**Juncheng Wei**- Affiliation: Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong
- MR Author ID: 339847
- ORCID: 0000-0001-5262-477X
- Email: wei@math.cuhk.edu.hk
- Received by editor(s): December 15, 1995
- Communicated by: Jeffrey Rauch
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**125**(1997), 3235-3242 - MSC (1991): Primary 35B40, 35B45; Secondary 35J40
- DOI: https://doi.org/10.1090/S0002-9939-97-04211-1
- MathSciNet review: 1443172