Double phase problems and a discontinuity property of the spectrum

Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš

Published 2019-06-05Version 1

We consider a nonlinear eigenvalue problem driven by the sum of $p$ and $q$-Laplacian. We show that the problem has a continuous spectrum. Our result reveals a discontinuity property for the spectrum of a parametric ($p,q$)-differential operator as the parameter $\beta\rightarrow 1^-$.