Nonexistence results for elliptic differential inequalities with a potential in bounded domains

TL;DR

This paper investigates how the behavior of potential functions at the boundary of bounded domains influences the nonexistence of nonnegative solutions to elliptic differential inequalities, providing new insights in both Euclidean and Riemannian settings.

Contribution

It introduces new nonexistence results for elliptic inequalities considering boundary potential behavior, extending previous work to Riemannian manifolds.

Findings

Boundary behavior of potential affects solution existence

Nonexistence results established for bounded domains

Results apply to both Euclidean and Riemannian manifolds

Abstract

In this paper we are concerned with a class of elliptic differential inequalities with a potential in bounded domains both of $\mathbf{R}^m$ and of Riemannian manifolds. In particular, we investigate the effect of the behavior of the potential at the boundary of the domain on nonexistence of nonnegative solutions.