Nonexistence of solutions to $Δ_pu+Δ_qu+u^s|\nabla u|^t\leq 0$ on geodesically complete noncompact Riemannian manifolds
Year: 2026
Type: preprint
Abstract: In this paper, we consider the inequality $Δ_pu+Δ_qu+u^s|\nabla u|^t\leq 0$ on geodesically complete noncompact Riemannian manifolds. By a test function argument, we establish Liouville-type theorems under the upper bound of volume of geodesic ball. In the Euclidean space $\mathbb{R}^n$, we obtain new nonexistence results which extend the result of Bhakta-Biswas-Filippucci \cite{BBF}. In particular, we have addressed the influence of the higher order term for $s<0$. At last, we present some examples to illustrate sharpness in some cases.
Source: arXiv (Cornell University)
Author: Zhao, Biqiang
Institution: Peking University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213594426