### A nonlocal elliptic equation in a bounded domain

The existence of a positive solution to the Dirichlet boundary value problem for the second order elliptic equation in divergence form $-{\sum}_{i,j=1}^{n}{D}_{i}\left({a}_{ij}{D}_{j}u\right)=f(u,{\int}_{\Omega}g\left({u}^{p}\right))$, in a bounded domain Ω in ℝⁿ with some growth assumptions on the nonlinear terms f and g is proved. The method based on the Krasnosel’skiĭ Fixed Point Theorem enables us to find many solutions as well.