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) Fucik eigenvalues on the first curve of the Fucik 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.
Highlights
Let Ω ⊂ RN be a bounded domain, N ≥ 2
The Fučík spectrum of -Δ on W01,2( ) is defined as a set Σ of those (l+, l-) Î R2 such that the Dirichlet problem
Following [1, p. 15], we call the elements of Σ \ ({l1} × R ∪ R × {l1}) nontrivial Fučík eigenvalues
Summary
Let Ω ⊂ RN be a bounded domain, N ≥ 2. The Fučík spectrum of -Δ on W01,2( ) is defined as a set Σ of those (l+, l-) Î R2 such that the Dirichlet problem It was proved in [2] that C is a continuous and strictly decreasing curve which contains the point (l2, l2) and which is symmetric with respect to the diagonal. We show that the point of intersection of this line and C corresponds to the critical value of some constrained functional
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