Asymptotic analysis and sign changing bubble towers for Lane-Emden\n problems

We consider the semilinear Lane-Emden problem in a smooth bounded domain of\nthe plane. The aim of the paper is to analyze the asymptotic behavior of sign\nchanging solutions as the exponent p of the nonlinearity goes to infinity.\nAmong other results we show, under some symmetry assumptions on the domain,\nthat the positive and negative parts of a family of symmetric solutions\nconcentrate at the same point, as p goes to infinity, and the limit profile\nlooks like a tower of two bubbles given by a superposition of a regular and a\nsingular solution of the Liouville problem in the plane.\n