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

DOI:
https://doi.org/10.1090/S0002-9939-97-04211-1

MathSciNet review:
1443172

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Abstract | References | Similar Articles | Additional Information

Abstract: We present the exact multiplicity results for some nonlinear elliptic equations in balls of radius . We prove that there is a critical value such that, for , the equation has no solution; when , it has exactly one solution; when , 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