Tohoku Mathematical Journal
2018

September
SECOND SERIES VOL. 70, NO. 3

Tohoku Math. J.
70 (2018), 339-352

Title ON A CLASS OF SINGULAR SUPERLINEAR ELLIPTIC SYSTEMS IN A BALL

Author Dang Dinh Hai

(Received September 3, 2015, revised April 5, 2016)
Abstract. We establish the existence of large positive radial solutions for the elliptic system

\[ \left\{ \begin{array}{c} -\Delta u=\lambda f(v) \text{in} B\\ -\Delta v=\lambda g(u) \text{in} B\\ u=v=0\enspace \text{on} \partial B \end{array} \right. \]

when the parameter $\lambda>0$ is small, where $B$ is the open unit ball $\mathbb{R}^N,N>2, f,g:(0,\infty) \rightarrow \mathbb{R}$ are possibly singular at 0 and $f(u) \sim u^p,g(v) \sim v^q$ at $\infty$ for some $p,q>0$ with $pq>1$. Our approach is based on fixed point theory in a cone.

Mathematics Subject Classification. Primary 35J57; Secondary 35J75.

Key words and phrases. Singular elliptic systems, positive radial solutions.

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