Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models
Stability and qualitative properties of radial solutions of the Lane-Emden-Fowler equation on Riemannian models
复制标题
黎曼模型上 Lane-Emden-Fowler 方程径向解的稳定性和定性性质
DOI：
10.1016/j.matpur.2013.10.012
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
G. Grillo
中科院分区：
文献类型：
--
作者：
E. Berchio;A. Ferrero;G. Grillo
研究了Lane-Emden-Fowler方程− Δ g u=| u| p− 1 u在一类维数n <$3的黎曼模型（M，g）中，其中包括经典的双曲空间H n以及截面曲率无界的流形。临界Sobolev指数影响解的符号性质和渐近行为，而Joseph-Lundgren指数则影响解的稳定性。
We study existence, uniqueness and stability of radial solutions of the Lane–Emden–Fowler equation− Δ 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.