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Zbl 1045.35025
Garc\'ia-Melián, Jorge; Suárez, Antonio
Existence and uniqueness of positive large solutions to some cooperative elliptic systems.
(English)
[J] Adv. Nonlinear Stud. 3, No. 2, 193-206 (2003). ISSN 1536-1365

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.
[Josef Dibl{\'\i}k (Brno)]
MSC 2000:
*35J55 Systems of elliptic equations, boundary value problems
35B40 Asymptotic behavior of solutions of PDE

Keywords: cooperative systems; boundary blow up; sub and supersolution; distance function

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