On nonnegative solutions of the differential inequality ${\mathrm{\Delta }}_{p}u+{\mathrm{\Delta }}_{q}u+V(x)u^s\le 0$ on Riemannian manifolds

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.