On positive solutions of nonlocal and nonvariational elliptic problems (Q1765209)

The author deals with the partial elliptic problem \[ \begin{cases} -a(\int_\Omega|u|^q dx)\,\Delta u= H(x) f(u)\quad &\text{in }\Omega,\\ u= 0\quad &\text{on }\partial\Omega,\end{cases}\tag{1} \] where \(a\), \(H\), \(f\) are given functions, \(q\geq 1\) and \(\Omega\) is a bounded domain of \(\mathbb R^N\). Using a comparison principle and Schaefer's fixed point theorem the author proves existence at least one positive solution for (1).