Memoirs of the American Mathematical Society 2010; 72 pp; softcover Volume: 208 ISBN10: 0821847260 ISBN13: 9780821847268 List Price: US$68 Individual Members: US$40.80 Institutional Members: US$54.40 Order Code: MEMO/208/976
 The authors provide a complete classification of the radial solutions to a class of reaction diffusion equations arising in the study of thermal structures such as plasmas with thermal equilibrium or no flux at the boundary. In particular, their study includes rapidly growing nonlinearities, that is, those where an exponent exceeds the critical exponent. They describe the corresponding bifurcation diagrams and determine existence and uniqueness of ground states, which play a central role in characterizing those diagrams. They also provide information on the stabilityunstability of the radial steady states. Table of Contents  Introduction
 Bifurcation diagrams
 Oscillation properties
 Ground states
 Stability of thermal structures
 Proof of main theorems
 The degenerate case, \(k=1\)
 Appendix 1. The conservative case \((N=1)\)
 Appendix 2. Pohozaev identity
 Bibliography
