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Maximum and antimaximum principles beyond the first eigenvalue

par Gossez, Jean-Pierre ;de Thelin, F.;Fleckinger, J.
Référence Differential and integral equations, 22, page (815-828)
Publication Publié, 2009

Article révisé par les pairs

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Résumé :

We consider the Dirichlet problem (*)-Δu = μu + f in Ω, u = 0 on dΩ. Let λ be an eigenvalue, with Φ an associated eigenfunction. Under suitable assumptions on f and on the nodal domains of Φ, we show that, if μ is sufficiently close to λ, then the solution u of (*) has the same number of nodal domains as Φ, and moreover the nodal domains of u appear as small deformations of those of Φ.