Positive solutions for a class of nonlocal problems with possibly singular nonlinearity (Q2675382)

The paper is focused on the elliptic equation with homogeneous Dirichlet boundary conditions \[ \left\{\begin{array}{l} -\Delta u=f\left(u,\displaystyle\int_{\Omega}|u|^p\,dx\right)\text{ in }\Omega,\\ u=0\text{ on }\partial \Omega, \end{array}\right.\tag{1} \] where \(p\ge 1\), \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) with smooth boundary, and the nonlinear reaction term \(f\) is a continuous function which can have multiple singularities in the second variable. By using fixed point arguments, the authors prove the existence of multiple positive solutions for problem \((1)\).