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Existence and uniqueness of positive large solutions to some cooperative elliptic systems. (English) Zbl 1045.35025
Positive solutions to cooperative elliptic systems $$-\Delta u=\lambda u-u^2+buv,\qquad -\Delta v=\mu v-v^2+cuv$$ in a bounded smooth domain $\Omega\subset \Bbb R^N$ $(\lambda, \mu\in \Bbb R$, $b,c>0)$ which blow up on the boundary $\partial \Omega$, are considered. The authors prove results concerning their existence and nonexistence, and give sufficient conditions for uniqueness. Also an exact estimation of the behaviour of the solution near the boundary is given.

35J55Systems of elliptic equations, boundary value problems (MSC2000)
35B40Asymptotic behavior of solutions of PDE