A Choquard‐type equation with a singular absorption nonlinearity in two dimensions

Abstract

In this article, we show the existence of a nonnegative solution to the singular problem posed in a bounded domain in (see below). We achieve this by approximating the singular function by a function , which pointwisely converges to as . Using variational techniques, the perturbed equation is shown to have a solution when the parameter is small enough. Letting and proving a pointwise gradient estimate, we show that the solution converges to a nontrivial nonnegative solution of the original problem .