IUMJ

Title: Isolated singularities of nonlinear elliptic inequalities. II. Asymptotic behavior of solutions

Authors: Steven D. Taliaferro

Issue: Volume 55 (2006), Issue 6, 1791-1812

Abstract:

We give conditions on a continuous function $f \colon (0,\infty) \to (0,\infty)$ which guarantee that every $C^{2}$ positive solution $u(x)$ of the differential inequalities \[ 0 \le -\Delta u \le f(u) \] in a punctured neighborhood of the origin in $\mathbb{R}^n$ ($n \ge 2$) is asymptotically radial (or asymptotically harmonic) as $|x| \to 0^{+}$.