On a radial positive solution to a nonlocal elliptic equation - Fijalkowski, Piotr; Przeradzki, Bogdan (Topological Methods in Nonlinear Analysis, 2003)
The existence of a solution to the Dirichlet boundary value problem fornonlinear Poisson equations with the nonlocal nonlinear term$$-Δ u=f\bigg(u,\int (g° u)\bigg),\quad u\vert\partial U=0,$$is proved by means of fixed point theorems for increasing compact operators.