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

We study the inequality −Δu−μ|x|2u≥(|x|−α⁎up)uq in an unbounded cone CΩρ⊂RN (N≥2) generated by a subdomain Ω of unit sphere SN−1⊂RN, p,q,ρ>0, μ∈R and 0≤α<N. In above, |x|−α⁎up denotes standard convolution operator CΩρ. discuss existence nonexistence positive solutions terms N,p,q,α,μ Ω. Extensions to systems inequalities are also investigated.