# Singular solutions of elliptic equations with iterated exponentials

## TL;DR

This paper constructs positive singular solutions for a class of elliptic equations involving iterated exponentials, extending previous work to more complex nonlinearities and analyzing their behavior near singularities.

## Contribution

It introduces a method to construct and analyze singular solutions for elliptic equations with iterated exponential nonlinearities, expanding the understanding of such equations.

## Key findings

- Constructed positive singular solutions with prescribed behavior.
- Extended previous results to iterated exponential nonlinearities.
- Provided a framework for analyzing solutions near singularities.

## Abstract

We construct positive singular solutions for the problem $-\Delta u=\lambda \exp (e^u)$ in $B_1\subset \mathbb{R}^n$ ($n\geq 3$), $u=0$ on $\partial B_1$, having a prescribed behaviour around the origin. Our study extends the one in Y. Miyamoto [Y. Miyamoto, A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth. J. Differential Equations \textbf{264} (2018), 2684--2707] for such nonlinearities. Our approach is then carried out to elliptic equations featuring iterated exponentials.