## Differential and Integral Equations

### A note on radial symmetry of positive solutions for semilinear elliptic equations in $\mathbb{R}^n$

Yūki Naito

#### Abstract

Symmetry properties of positive solutions of the equations $$\Delta u + \phi(|x|)f(u) = 0$$ in $\mathbb{R}^n$ are considered. We employ the moving plane method based on the maximum principle on unbounded domains to obtain new results on symmetr

#### Article information

Source
Differential Integral Equations, Volume 11, Number 6 (1998), 835-845.

Dates
First available in Project Euclid: 30 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367329479

Mathematical Reviews number (MathSciNet)
MR1659264

Zentralblatt MATH identifier
1074.35506

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.

#### Citation

Naito, Yūki. A note on radial symmetry of positive solutions for semilinear elliptic equations in $\mathbb{R}^n$. Differential Integral Equations 11 (1998), no. 6, 835--845. https://projecteuclid.org/euclid.die/1367329479