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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 Δgu=f(r,u)-\Delta_g u=f(r,u) posed on a class of Riemannian models (M,g)(M,g) of dimension n2n\ge 2 which include the classical hyperbolic space Hn\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)f(r,u), where rr denotes the geodesic distance from the pole of MM

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