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≥2 which include the classical hyperbolic space 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.
Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models
BERCHIO, Elvise;FERRERO, ALBERTO;
2015-01-01
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≥2 which include the classical hyperbolic space 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.File in questo prodotto:
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