Nonexistence Results for Semilinear Equations in Carnot Groups

Abstract

In this paper, following [3], we provide some nonexistence results for semilinear equations in the the class of Carnot groups of type ★.This class, see [20], contains, in particular, all groups of step 2; like the Heisenberg group, and also Carnot groups of arbitrarly large step. Moreover, we prove some nonexistence results for semilinear equations in the Engel group, which is the simplest Carnot group that is not of type ★.

Keywords

• semilinear pdes
• carnot groups
• nonexistence results
• 35r03
• 35j61
• 35b06