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.
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Berchio, E., Ferrero, A. & Vallarino, M. Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models. Nonlinear Differ. Equ. Appl. 22, 1167–1193 (2015). https://doi.org/10.1007/s00030-015-0318-1
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DOI: https://doi.org/10.1007/s00030-015-0318-1