Multiple solutions for a semilinear elliptic equation

Authors:
Manuel A. del Pino and Patricio L. Felmer

Journal:
Trans. Amer. Math. Soc. **347** (1995), 4839-4853

MSC:
Primary 35J65; Secondary 58E05

MathSciNet review:
1303117

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a bounded, smooth domain in , . We consider the problem of finding nontrivial solutions to the elliptic boundary value problem

Let denote the interior of the set where vanishes in . We assume a.e. on and consider the eigenvalues and of the Dirichlet problem in and respectively. We prove that no nontrivial solution of the equation exists if satisfies, for some ,

For the proof of these results we use a variational approach. In particular, the existence result takes advantage of the even character of the associated functional.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1303117-5

Keywords:
Variational method,
multiplicity,
uniqueness,
blow up of solutions

Article copyright:
© Copyright 1995
American Mathematical Society