Year: 2026
Type: preprint
Abstract: In this work, we establish existence and regularity results for solutions to nonlinear nonlocal equations of the form $f(Δ)u = U(x,u)$ and $f(Δ_{g})u = U(x,u)$ in Euclidean and Riemannian settings, respectively. We prove existence results across three distinct geometric scenarios: bounded domains in $\mathbb{R}^n$, perturbed equations on compact Riemannian manifolds, and noncompact Cartan-Hadamard manifolds under suitable geometric curvature conditions.
Source: arXiv (Cornell University)
Author: Castellanos, Santiago
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223109296