Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models

Abstract

We consider least energy solutions to the nonlinear equation $${-\Delta_g u=f(r,u)}$$ posed on a class of Riemannian models (M,g) of dimension $${n \geq 2}$$ which include the classical hyperbolic space $${\mathbb{H}^{n}}$$ as well as manifolds with unbounded sectional geometry. Partial symmetry and existence of least energy solutions is proved for quite general nonlinearities f(r, u), where r denotes the geodesic distance from the pole of M.