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Proceedings of the American Mathematical Society

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

 

 

Exact multiplicity for some
nonlinear elliptic equations in balls


Author: Juncheng Wei
Journal: Proc. Amer. Math. Soc. 125 (1997), 3235-3242
MSC (1991): Primary 35B40, 35B45; Secondary 35J40
MathSciNet review: 1443172
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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.


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Additional Information

Juncheng Wei
Affiliation: Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong
Email: wei@math.cuhk.edu.hk

DOI: https://doi.org/10.1090/S0002-9939-97-04211-1
Keywords: Exact multiplicity, nonlinear elliptic equations
Received by editor(s): December 15, 1995
Communicated by: Jeffrey Rauch
Article copyright: © Copyright 1997 American Mathematical Society