On symmetry in semi-linear elliptic systems with nonnegative solutions

Abstract

It is shown in⁸ that positive solutions to the semilinear elliptic system

are radially symmetric if f is of C¹ and quasimonotone increasing, is a bounder domain in Rⁿ with n>1. In this paper we show that if is a ball in Rⁿ then all non-negative nontrivial solutions of (1) are positive and therefore radially symmetric.

Keywords:

• elliptic systems
• nonnegatlbe rolutions.
• symmetry.
• mourt?.n pass