Convergence properties of modular eigenfunctions for the p(⋅)p(⋅)-Laplacian

The variation of the first Dirichlet eigenfunction for the modular p(⋅)p(⋅)-Laplacian is studied as a generalization of the constant case. The stability of the eigenfunctions under perturbations of the norm of the underlying spaces (i.e., with respect to perturbations of the exponent p(⋅)p(⋅)) is observed.