We consider the semilinear Lane–Emden problem
where and is a smooth bounded domain of . The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of (), as . Among other results we show, under some symmetry assumptions on , that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as , and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of the Liouville problem in .
Cite this article
Francesca De Marchis, Isabella Ianni, Filomena Pacella, Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems. J. Eur. Math. Soc. 17 (2015), no. 8, pp. 2037–2068DOI 10.4171/JEMS/549