Conditions for the existence of solutions to a quasilinear inequality in half-space (Q1581468)

The authors establish conditions for the existence of solutions to a quasilinear differential inequality \[ \frac{\partial u}{\partial t}\geq L[u^p]+u^q,\quad t>0,\quad x\in\mathbb{R}^n, \] where \(p=\text{constant}\geq 1\) and \(q=\text{constant}>1\). For related results see the papers of \textit{H. Fujita} [J. Fac. Sci., Univ. Tokyo, Sect. I 13, 109-124 (1966; Zbl 0163.34002)] and \textit{K. Hayakawa} [Proc. Japan Acad. 49, 503-505 (1973; Zbl 0281.35039)].