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A remark on uniqueness of large solutions for elliptic systems of competitive type. (English) Zbl 1131.35015
Summary: We prove that the semilinear system Δu=a(x)u p v q , Δv=b(x)u r v s in a smooth bounded domain Ω N has a unique positive solution with the boundary condition u=v=+ on Ω, provided that p,s>1, q,r>0 and (p-1)(s-1)-qr>0. The main novelty is imposing a growth on the possibly singular weights a(x), b(x) near Ω, rather than requiring them to have a precise asymptotic behaviour.
35J60Nonlinear elliptic equations
35J65Nonlinear boundary value problems for linear elliptic equations