Lower bound for Orlicz Eigenvalues

ARIEL SALORT

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

AMER INST MATHEMATICAL SCIENCES

Lugar: springfield; Año: 2022

1078-0947

In this article we consider the following weighted nonlinear eigenvalue problem for the g−Laplacianwith Dirichlet boundary conditions. Here w is a suitable weight and g = G′ and h = H′ are appropriated Young functions satisfying the so called ∆′ condition, which includes for instance logarithmic perturbation of powers and different power behaviors near zero and infinity. We prove several properties on its spectrum, being our main goal to obtain lower bounds of eigenvalues in terms of G, H, w and the normalization µ of the corresponding eigenfunctions. We introduce some new strategies to obtain results that generalize several inequalities from the literature of p−Laplacian type eigenvalues