# American Institute of Mathematical Sciences

March  2016, 15(2): 549-562. doi: 10.3934/cpaa.2016.15.549

## Elliptic systems with boundary blow-up: existence, uniqueness and applications to removability of singularities

 1 Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271. La Laguna 2 Departamento de Análisis Matemático, Universidad de Alicante, Ap 99, 03080, Alicante 3 Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271 -- La Laguna, Spain

Received  July 2015 Revised  December 2015 Published  January 2016

In this paper we consider the elliptic system $\Delta u = u^p -v^q$, $\Delta v= -u^r +v^s$ in $\Omega$, where the exponents verify $p,s>1$, $q,r>0$ and $ps>qr$, and $\Omega$ is a smooth bounded domain of $R^N$. First, we show existence and uniqueness of boundary blow-up solutions, that is, solutions $(u,v)$ verifying $u=v=+\infty$ on $\partial \Omega$. Then, we use them to analyze the removability of singularities of positive solutions of the system in the particular case $qr\leq 1$, where comparison is available.
Citation: Jorge García-Melián, Julio D. Rossi, José C. Sabina de Lis. Elliptic systems with boundary blow-up: existence, uniqueness and applications to removability of singularities. Communications on Pure & Applied Analysis, 2016, 15 (2) : 549-562. doi: 10.3934/cpaa.2016.15.549
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