Blow‐Up Results for Some Type of Partial Differential Equations in Exterior Domains in the Hyperbolic Space

ABSTRACT In this paper, we investigate the existence of global nontrivial weak solutions to certain partial differential systems defined in the exterior domain of hyperbolic space. We establish sufficient conditions for the nonexistence of such global solutions, providing insights into the behavior of these solutions in the context of hyperbolic geometry. Our results highlight the challenges in the existence of global solutions in non‐Euclidean settings.