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

Francesca De Marchis; Isabella Ianni; Filomena Pacella — 2015

Journal of the European Mathematical Society

We consider the semilinear Lane–Emden problem where $p > 1$ and $Ω$ is a smooth bounded domain of $ℝ^{2}$ . The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of $(_{p})$ , as $p \to + \infty$ . Among other results we show, under some symmetry assumptions on $Ω$ , that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as $p \to + \infty$ , 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...

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