Can it be proved that two elliptic operators with Robin boundary conditions generate an interval $P$-matrix?
$$ -a\Delta u_i = f_i, \quad a\frac{\partial u_i}{\partial n} + bu_i = 0 $$ $$ -a\Delta v_i = f_i, \quad a\frac{\partial v_i}{\partial n} + cv_i = 0 $$
Here, $f_i \geq 0$ are linear independent functions, $0 < b \leq c$, so $0 \leq v_i \leq u_i$.
Let $B_{ji} = (f_j, u_i)$, $C_{ji} = (f_j, v_i)$, and $C_{ji} \leq A_{ji} \leq B_{ji}$.
It is true that $A$ is always a $P$-matrix?
