Classification of radial solutions to −Δgu = eu on Riemannian models

We provide a complete classification with respect to asymptotic behaviour, stability and intersections properties of radial smooth solutions to the equation -Agu = eu on Riemannian model manifolds (M, g) in dimension N > 2. Our assumptions include Riemannian manifolds with sectional curvatures bounded or unbounded from below. Intersection and stability properties of radial solutions are influenced by the dimen-sion N in the sense that two different kinds of behaviour occur when 2 < N < 9 or N > 10, respectively. The crucial role of these dimensions in classifying solutions is well-known in Euclidean space; here the analysis highlights new properties of solutions that cannot be observed in the flat case. (c) 2023 Elsevier Inc. All reserved.