Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models

Elvise Berchio; Alberto Ferrero; Gabriele Grillo

doi:10.1016/j.matpur.2013.10.012

Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models

Elvise Berchio
, Alberto Ferrero
, Gabriele Grillo

Department of Science and Technological Innovation

Research output: Contribution to journal › Article › peer-review

Abstract

We study existence, uniqueness and stability of radial solutions of the Lane-Emden-Fowler equation -δ_gu=|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.

Original language	English
Pages (from-to)	1-35
Number of pages	35
Journal	Journal des Mathematiques Pures et Appliquees
Volume	102
Issue number	1
DOIs	https://doi.org/10.1016/j.matpur.2013.10.012
Publication status	Published - Jul 2014

Keywords

Asymptotics of solutions
Joseph-Lundgren exponent
Lame-Emden-Fowler equations
Negatively curved manifolds
Riemannian models
Stability of solutions

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10.1016/j.matpur.2013.10.012

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title = "Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models",

abstract = "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.",

keywords = "Asymptotics of solutions, Joseph-Lundgren exponent, Lame-Emden-Fowler equations, Negatively curved manifolds, Riemannian models, Stability of solutions",

author = "Elvise Berchio and Alberto Ferrero and Gabriele Grillo",

note = "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 viscosit{\`a}, geometrici e di controllo per modelli diffusivi nonlineari”. ",

year = "2014",

month = jul,

doi = "10.1016/j.matpur.2013.10.012",

language = "English",

volume = "102",

pages = "1--35",

journal = "Journal des Mathematiques Pures et Appliquees",

issn = "0021-7824",

publisher = "Elsevier Masson s.r.l.",

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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 -

Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models

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Keywords

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