Geometric Estimates of the First Eigenvalue of $(p,q)$-Elliptic Quasilinear System Under Integral Curvature Condition

Abstract

Consider (M,g) as a complete, simply connected Riemannian manifold. The aim of this paper is to provide various geometric estimates in different cases for the first eigenvalue of $(p,q)$-elliptic quasilinear system in both Dirichlet and Neumann conditions on Riemannian manifold. In some cases we add integral curvature condition and maybe we prove some theorems under other conditions.