On a Class of Integro‐Differential Equations Involving Subcritical, Critical, and Supercritical Nonlinearities

In this paper, we study a class of elliptic problems in the presence of a nonlocal term and a parameter. A careful analysis of the influence of the referred nonlocal term and the parameter on the existence and nonexistence of solution was carried out, where we considered different scenarios. Among our main contributions are: a identity for a class of elliptic integro‐differential problems (which produces some results of nonexistence of solutions) and an extensive study of the critical nonlocal problem, which includes the study of the double critical case. Some of the main tools used in the research were global and local minimization, mountain pass theorem, concentration compactness principle, sub‐supersolution method, and a Carl–Heikkilä fixed point theorem.