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Zbl 1162.35359
Garc\'ia-Melián, Jorge; Rossi, Julio D.
Boundary blow-up solutions to elliptic systems of competitive type. (English)
[J] J. Differ. Equations 206, No. 1, 156-181 (2004). ISSN 0022-0396

The elliptic system $\Delta u=u^pv^q$, $\Delta v=u^rv^s$, where $p,s>1$, $q,r>0$ is studied on smooth bounded domain $\Omega\subset \Bbb R^n$. Dirichlet type boundary conditions: $u=\lambda, v=\mu$ or $u=v=+\infty$ or $u=+\infty, v=\mu$ are considered with $\lambda,\mu>0$. Under certain hypotheses the existence and nonexistence of positive solutions is proved together with discussion of uniqueness and nonuniqueness. Moreover, the exact asymptotic behaviour of the solutions and their normal derivatives near $\partial \Omega$ is provided.
[Josef Dibl{\'\i}k (Brno)]

MSC 2000:: *35J55 Systems of elliptic equations, boundary value problems
35B45 A priori estimates
35J60 Nonlinear elliptic equations

Keywords: elliptic systems; boundary blow-up

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