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

E. Berchio; A. Ferrero; M. Vallarino

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arXiv · 1409.2748

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

E. Berchio·A. Ferrero·M. Vallarino

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Abstract

We consider least energy solutions to the nonlinear equation $-Δ_g u=f(r,u)$ posed on a class of Riemannian models $(M,g)$ of dimension $n\ge 2$ 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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E. Berchio, A. Ferrero, M. Vallarino. 2014-09-09. Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models. https://arxiv.org/abs/1409.2748

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