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Open Access Research

The first nontrivial curve in the fučĺk spectrum of the dirichlet laplacian on the ball consists of nonradial eigenvalues

Jiřĺ Benedikt1*, Pavel Drábek2 and Petr Girg1

Author affiliations

1 Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitnĺ 22, 306 14 Plzeň, Czech Republic

2 Department of Mathematics and N.T.I.S., Faculty of Applied Sciences, University of West Bohemia, Univerzitnĺ 22, 306 14 Plzeň, Czech Republic

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Citation and License

Boundary Value Problems 2011, 2011:27  doi:10.1186/1687-2770-2011-27

Published: 4 October 2011

Abstract

It is well-known that the second eigenvalue λ2 of the Dirichlet Laplacian on the ball is not radial. Recently, Bartsch, Weth and Willem proved that the same conclusion holds true for the so-called nontrivial (sign changing) Fučík eigenvalues on the first curve of the Fučík spectrum which are close to the point (λ2, λ2). We show that the same conclusion is true in dimensions 2 and 3 without the last restriction.

Keywords:
Fučík spectrum; The first curve of the Fučík spectrum; Radial and nonradial eigenfunctions