We study existence, uniqueness and stability of radial solutions of the Lane-Emden-Fowler equation -\Delta_g u=|u|^(p -1) u in a class of Riemannian models (M, g) of dimension n = 3 which includes the classical hyperbolic space H^n as well as manifolds with sectional curvatures unbounded below. Sign properties and asymptotic behavior of solutions are influenced by the critical Sobolev exponent while the so-called Joseph-Lundgren exponent is involved in the stability of solutions.
Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models
FERRERO, ALBERTO;
2014-01-01
Abstract
We study existence, uniqueness and stability of radial solutions of the Lane-Emden-Fowler equation -\Delta_g u=|u|^(p -1) u in a class of Riemannian models (M, g) of dimension n = 3 which includes the classical hyperbolic space H^n as well as manifolds with sectional curvatures unbounded below. Sign properties and asymptotic behavior of solutions are influenced by the critical Sobolev exponent while the so-called Joseph-Lundgren exponent is involved in the stability of solutions.File in questo prodotto:
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