Nonexistence results of solutions to systems of semilinear differential inequalities on the Heisenberg group

Abstract

We establish nonexistence results to systems of differential inequalities on the $\left(2N+1\right)$-Heisenberg group. The systems considered here are of the type $\left({\text{ES}}_m\right)$. These nonexistence results hold for $N$ less than critical exponents which depend on $p_i$ and ${\gamma }_i$, $1\le i\le m$. Our results improve the known estimates of the critical exponent.