On nonnegative solutions of the differential inequality $\Delta_pu+ \Delta_q u+V(x)u^s\leq 0$ on Riemannian manifolds

TL;DR

This paper investigates nonnegative solutions to a differential inequality involving the $(p,q)$-Laplacian on Riemannian manifolds, establishing Liouville-type theorems based on geometric and potential conditions.

Contribution

It introduces new Liouville-type theorems for the $(p,q)$-Laplacian inequality on manifolds, considering geometric and potential growth conditions.

Findings

Liouville-type theorems are proved under specific geometric and potential conditions.

Test function methods are used to derive nonexistence results.

Results depend on the behavior of the potential at infinity.

Abstract

In this paper, we are concerned with differential inequalities with $(p,q)$-Laplacian operator on Riemannian manifolds. Using a test function argument, we establish Liouville-type theorems under the manifold's geometry and the potential's behavior at infinity.