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Boundary blow-up solutions to elliptic systems of competitive type. (English) Zbl 1162.35359
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.

MSC:
35J55Systems of elliptic equations, boundary value problems (MSC2000)
35B45A priori estimates for solutions of PDE
35J60Nonlinear elliptic equations
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References:
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