On symmetry in elliptic systems

Abstract

We prove symmetry of positive solutions of quasimonotone elliptic systems. We show by counterexamples that quasimonotonicity of the systems and positivity of solutions are necessary for solutions to be symmetric. We consider solutions in both bounded domains and in the entire space. We also point out an error in a published paper

AMS(MOS):

• 35

Keywords:

• Quasimonotone elliptic systems
• maximum principles
• positive solutions
• radially symmetric solutions