Singular Solutions of Elliptic Equations with Iterated Exponentials

Abstract

We construct positive singular solutions for the problem $$-\Delta u=\lambda \exp (e^u)$$ in $$B_1\subset {\mathbb {R}}^n$$ ($$n\ge 3$$), $$u=0$$ on $$\partial B_1$$, having a prescribed behaviour around the origin. Our study extends the one in Miyamoto (J Differ Equ 264:2684–2707, 2018) for such nonlinearities. Our approach is then carried out to elliptic equations featuring iterated exponentials.