TY - JOUR
T1 - Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models
AU - Berchio, Elvise
AU - Ferrero, Alberto
AU - Grillo, Gabriele
N1 - Funding Information:
E. Berchio and A. Ferrero were partially supported by the PRIN 2008 grant “Aspetti geometrici delle equazioni alle derivate parziali e questioni connesse”. G. Grillo was partially supported by the PRIN 2009 grant “Metodi di viscosità, geometrici e di controllo per modelli diffusivi nonlineari”.
PY - 2014/7
Y1 - 2014/7
N2 - We study existence, uniqueness and stability of radial solutions of the Lane-Emden-Fowler equation -δgu=|u|p-1u in a class of Riemannian models (M, g) of dimension n≥3 which includes the classical hyperbolic space Hn 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.
AB - We study existence, uniqueness and stability of radial solutions of the Lane-Emden-Fowler equation -δgu=|u|p-1u in a class of Riemannian models (M, g) of dimension n≥3 which includes the classical hyperbolic space Hn 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.
KW - Asymptotics of solutions
KW - Joseph-Lundgren exponent
KW - Lame-Emden-Fowler equations
KW - Negatively curved manifolds
KW - Riemannian models
KW - Stability of solutions
UR - https://www.scopus.com/pages/publications/84901595969
U2 - 10.1016/j.matpur.2013.10.012
DO - 10.1016/j.matpur.2013.10.012
M3 - Article
SN - 0021-7824
VL - 102
SP - 1
EP - 35
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
IS - 1
ER -