Year: 2026
Type: preprint
Abstract: We study the Liouville property for nonnegative weak solutions of the $(p,q)$-Laplacian elliptic differential inequality $$Δ^{m}_{p}u(x)+Δ^{m}_{q}u(x)+V(x)u^{s}(x)\leq 0$$ and the associated parabolic differential inequality $$\partial_t u(x,t) \geq Δ^{m}_{p}u(x,t)+Δ^{m}_{q}u(x,t)+V(x,t)u^{s}(x,t)$$ on a forward geodesically complete noncompact Finsler measure space $(M,F,m)$ with finite reversibility. Under several sets of integral growth conditions on the positive potential function over certain annular domains, we prove that any nonnegative weak solution vanishes almost everywhere. The proofs of our results are essentially based on the nonlinear capacity method.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2192645024
OpenAlex ID: W7211888333