Growth of solutions of nonlinear degenerating elliptic inequalities in unbounded domains (Q5960212)

The author studies the behavior on the unbounded interval of solutions to the differential inequality \(Lu\geq f(u)\) in the half-space \(\,\Pi = \{x\in \mathbb R^n\: x_n>0\}\,\) with the initial condition \(u|_{\{x_n=0\}}\leq 0,\) where \(\,f(v)\in\mathbb C(\mathbb R)\), \(f\) is a monotone increasing function, \(\,f(v)>0\), if \(\,v>0\), and \(L\) is an elliptic operator. The theorem of the Phragmén-Lindelöf type is obtained for a semilinear elliptic operator.