A singular Gierer–Meinhardt system of elliptic equations in RNRN

In this paper, we study the existence and uniqueness of solution of the singular Gierer–Meinhardt system {−Δu+α(x)u=h1(x)1vq−Δv+β(x)v=h2(x)urvsu(x),v(x)⟶0 as |x|⟶∞u,v>0 in RN(N≥3)RN(N≥3), where α,β,h1,h2α,β,h1,h2 are given, not necessarily continuous functions, s∈]0,1[ and q,r>0q,r>0 such that r−s≤1r−s≤1. We establish the existence of the solution using Schauder’s fixed point theorem.