In this paper, we investigate the existence of positive solutions to the problem P \(\begin{aligned} \left\{ \begin{array}{lcl} -\Delta u=u^{q}\left( \lambda +\displaystyle {\int _{\Omega }K(x,y)f(u)dy}\right) ,\quad \text{ in } \quad \Omega \\ u=0, \quad \text{ on } \quad \partial \Omega \\ \end{array}\right. \end{aligned}\) where \(\Omega \subset {\mathbb {R}}^N\) , \(N\ge 1\) , is a bounded domain with smooth boundary, \(q\in (0,1)\) , \(\lambda \in {\mathbb {R}}\) and \(f:[0,\infty )\rightarrow {\mathbb {R}}\) , \(K:\Omega \times \Omega \rightarrow {\mathbb {R}}\) are nonnegative functions with \(K\in L^{\infty }(\Omega \times \Omega )\) and verifying other conditions that will be detailed below. Problems like (P) appear quite often in some models related to population dynamics, such that the integral nonlocal term on the right-hand side makes the problem closer to a real-world situation.
