Principal eigenvalue problem for infinity Laplacian in metric spaces

Abstract This article is concerned with the Dirichlet eigenvalue problem associated ∞ \infty -Laplacian in metric spaces. We establish a direct partial differential equation approach to find principal and eigenfunctions proper geodesic space without assuming any measure structure. provide an appropriate notion of solutions -eigenvalue show existence by adapting Perron’s method. Our method different from standard limit process via variational formulation for p p Euclidean space.