Elliptic inequalities with nonlinear convolution and Hardy terms in cone-like domains

We study the inequality -Delta u - mu|x|2u > (|x|-alpha * up)uq in an unbounded cone C rho omega subset of RN (N > 2) generated by a subdomain omega of the unit sphere SN-1 subset of RN, p, q, rho > 0, mu E R and 0 < alpha < N. In the above, |x|-alpha * up denotes the standard convolution operator in the cone C rho omega. We discuss the existence and nonexistence of positive solutions in terms of N, p, q, alpha, mu and omega. Extensions to systems of inequalities are also investigated.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).