Memoirs of the American Mathematical Society 2014; 85 pp; softcover Volume: 227 ISBN10: 0821890220 ISBN13: 9780821890226 List Price: US$71 Individual Members: US$42.60 Institutional Members: US$56.80 Order Code: MEMO/227/1068
 In this paper, the author considers semilinear elliptic equations of the form \(\Delta u \frac{\lambda}{x^2}u +b(x)\,h(u)=0\) in \(\Omega\setminus\{0\}\), where \(\lambda\) is a parameter with \(\infty<\lambda\leq (N2)^2/4\) and \(\Omega\) is an open subset in \(\mathbb{R}^N\) with \(N\geq 3\) such that \(0\in \Omega\). Here, \(b(x)\) is a positive continuous function on \(\overline \Omega\setminus\{0\}\) which behaves near the origin as a regularly varying function at zero with index \(\theta\) greater than \(2\). The nonlinearity \(h\) is assumed continuous on \(\mathbb{R}\) and positive on \((0,\infty)\) with \(h(0)=0\) such that \(h(t)/t\) is bounded for small \(t>0\). The author completely classifies the behaviour near zero of all positive solutions of equation (0.1) when \(h\) is regularly varying at \(\infty\) with index \(q\) greater than \(1\) (that is, \(\lim_{t\to \infty} h(\xi t)/h(t)=\xi^q\) for every \(\xi>0\)). In particular, the author's results apply to equation (0.1) with \(h(t)=t^q (\log t)^{\alpha_1}\) as \(t\to \infty\) and \(b(x)=x^\theta (\log x)^{\alpha_2}\) as \(x\to 0\), where \(\alpha_1\) and \(\alpha_2\) are any real numbers. Table of Contents  Introduction
 Main results
 Radial solutions in the power case
 Basic ingredients
 The analysis for the subcritical parameter
 The analysis for the critical parameter
 Illustration of our results
 Appendix A. Regular variation theory and related results
 Bibliography
