Radially symmetric solutions to a Dirichlet problem involving critical exponents

Authors:
Alfonso Castro and Alexandra Kurepa

Journal:
Trans. Amer. Math. Soc. **343** (1994), 907-926

MSC:
Primary 35B05; Secondary 35J65

DOI:
https://doi.org/10.1090/S0002-9947-1994-1207581-0

MathSciNet review:
1207581

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we answer, for , the question raised in [1] on the number of radially symmetric solutions to the boundary value problem , , , , where is the Laplacean operator and . Indeed, we prove that if , then for any this problem has only finitely many radial solutions. For we show that, for each , the set of radially symmetric solutions is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1207581-0

Keywords:
Critical exponent,
radially symmetric solutions,
Dirichlet problem,
nodal curves,
bifurcation

Article copyright:
© Copyright 1994
American Mathematical Society