On the growth of superharmonic functions near an isolated singularity. I (Q1818849)

The author studies the growth near the origin of \(C^2\) positive solutions \(u(x)\) of \[ af(u)< -\Delta u<bf(u) \quad\text{in }\Omega, \] where \(\Omega\subset \mathbb{R}^n\) is a punctured neighborhood of the origin, \(a\) and \(b\) are positive constants and \(f:(0,\infty)\to (0,\infty)\) is a continuous function. For related results see the papers of \textit{L. A. Caffarelli, B. Gidas} and \textit{J. Spruck} [Commun. Pure Appl. Math. 42, 271-297 (1989; Zbl 0702.35085)] and \textit{Chiun-Chuan Chen} and \textit{Chang-Shou Lin} [Commun. Pure Appl. Math. 50, 971-1017 (1997)].