A note on positive eigenfunctions and hidden convexity

Lorenzo Brasco (1) , Giovanni Franzina (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 Department of mathematics/Dipartimento di Matematica [Univ. Trento]

We give a simple convexity-based proof of the following fact: the only eigenfunction of the $p-$Laplacian that does not change sign is the first one. The method of proof covers as well more general nonlinear eigenvalue problems.

Mots clés: Nonlinear eigenvalue problems; uniqueness of eigenfunctions

Domaines: Equations aux dérivées partielles [math.AP]

Lorenzo Brasco, Giovanni Franzina. A note on positive eigenfunctions and hidden convexity. 2012. ⟨hal-00706164v2⟩