The first nontrivial curve in the fu??k spectrum of the dirichlet laplacian on the ball consists of nonradial eigenvalues

摘要

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) Fu?ík eigenvalues on the first curve of the Fu?ík 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.