Symmetry of positive solutions of \(\Delta u + u^ p = 0\) in \(\mathbf R^ n\). (English) Zbl 0844.35028

Zou, Henghui

J. Differ. Equations 120, No. 1, 46-88 (1995).

The Lane-Emden equation \(\Delta u+ u^p= 0\) is considered in \(\mathbb{R}^n\), \(n> 2\). Conditions are established for a nontrivial nonnegative solution of this equation to be radially symmetric. Hölder type and Lipschitz type estimates and the Alexandroff-Serrin moving plane method are applied.

Reviewer: V.N.Gusyatnikova (Pereslavl’-Zalesskij)

MSC:

35J60	Nonlinear elliptic equations
35B05	Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

moving plane method; radially symmetric solution