Nonlocal problem with critical exponential nonlinearity of the convolution type: A non‐resonant case

Abstract In this paper, we study the following class of weighted Choquard equations: where is a bounded domain with smooth boundary, and is a parameter. We assume that is a real‐valued continuous function satisfying critical exponential growth in the Trudinger–Moser sense, and is the primitive of . Let be a positive real‐valued continuous weight, which can be singular at zero. Our main goal is to prove the existence of a nontrivial solution for all parameter values except when coincides with any of the eigenvalues of the operator .