Blow-up analysis, existence and qualitative properties of solutions for the two-dimensional Emden-Fowler equation with singular potential

Motivated by the study of a two-dimensional point vortex model, we analyse the following Emden-Fowler type problem with singular potential: [GRAPHICS] where V(x) = K (x)/vertical bar x vertical bar(2 alpha) with alpha is an element of (0, 1), 0<a,<= K(x)<= b<+infinity, for all x is an element of Omega and parallel to del K parallel to(infinity)<= C. We first extend various results, already known in case alpha <= 0, to cover the case alpha is an element of(0, 1). In particular, we study the concentration-compactness problem and the mass quantization properties, obtaining some existence results. Then, by a special choice of K, we include the effect of the angular momentum in the system and obtain the existence of axially symmetric one peak non-radial blow-up solutions. Copyright (C) 2007 John Wiley & Sons, Ltd.