Coupled Elliptic Systems with Sublinear Growth - Ubilla-Lopez, P; Arratia-Parra, J (Elsevier Ltd, 2025)
Consider the coupled elliptic system −Δu+u=ρ1(x)up1+λvinRN−Δv+v=ρ2(x)vp2+λuinRN,u(x),v(x)→0as|x|→∞.We observe that in 2008, A. Ambrosetti, G. Cerami and D. Ruiz proved the existence of positive bound and ground states in the case λ∈(0,1), p1=p=p2, 1<p<2∗−1, ρ1(x) and ρ2(x) tends to one at infinity. In this work we complement their result, because we show that the previous system has no solutions when 0<p1,p2<1, as well as we establish sharp hypotheses on the powers 0<p1,p2 the parameter λ and the weights ρ1(x), ρ2(x) that will allow us to obtain the existence and uniqueness of a positive bounded solution. © 2024 Elsevier Ltd