par de Thelin, F.;Gossez, Jean-Pierre ;Fleckinger, J.
Référence Differential and integral equations, 24, page (389-400)
Publication Publié, 2011
Article révisé par les pairs
Résumé : We consider the Dirichlet problem (*) -Δu = μu + f in Ω, u = 0 on Ω, with Ω either a bounded smooth convex domain in R2, or a ball or an annulus in RN. Let λ2 be the second eigenvalue, with φ2 an associated eigenfunction. Although the two nodal domains of φ2 do not satisfy the interior ball condition, we are able to prove under suitable assumptions that, if μ is suffciently close to λ2, then the solution u of (*) also has two nodal domains which appear as small deformations of the nodal domains of φ2. For N = 2, use is made in the proof of several results relative to the Payne conjecture.