Singular solutions of elliptic equations with iterated exponentials
Abstract
We construct positive singular solutions for the problem $\Delta u=\lambda \exp (e^u)$ in $B_1\subset \mathbb{R}^n$ ($n\geq 3$), $u=0$ 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), 26842707] for such nonlinearities. Our approach is then carried out to elliptic equations featuring iterated exponentials.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 arXiv:
 arXiv:1906.05025
 Bibcode:
 2019arXiv190605025G
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 15 pages