Existence and uniqueness of positive solutions to the boundary blow-up problem for an elliptic system
The authors deal with a system of semilinear elliptic equation of the form \[ \begin{gathered} -\Delta u= u(a_1- b_1 u^m- c_1 v^n),\quad x\in\Omega,\\ -\Delta v= v(a_2- b_2 u^p- c_2 v^q),\quad x\in\Omega,\end{gathered}\tag{1} \] where \(\Omega\subset\mathbb{R}^d\) is a bounded domain of class \(C^{2,\alpha}\) for some \(\alpha\in (0,1)\). The main goal of this paper is to study the influence of the parameters \(a_i\), \(b_i\), \(c_i\) \((i= 1,2)\) and the exponents \(m\), \(n\), \(p\), \(q\) on the existence, uniqueness and asymptotic behaviour of positive solutions to the system (1) under different boundary conditions.
scientific article; zbMATH DE number 5132874