Boundary blow-up solutions to elliptic systems of competitive type

@article{GarcaMelin2004BoundaryBS,
  title={Boundary blow-up solutions to elliptic systems of competitive type},
  author={J. Garc{\'i}a-Meli{\'a}n and J. Rossi},
  journal={Journal of Differential Equations},
  year={2004},
  volume={206},
  pages={156-181}
}
Abstract We consider the elliptic system Δ u = u p v q , Δ v = u r v s in Ω , where p , s > 1 , q , r > 0 , and Ω ⊂ R N is a smooth bounded domain, subject to different types of Dirichlet boundary conditions: (F) u = λ , v = μ , (I) u = v =+ ∞ and (SF) u =+ ∞ , v = μ on ∂ Ω , where λ , μ > 0 . Under several hypotheses on the parameters p , q , r , s , we show existence and nonexistence of positive solutions, uniqueness and nonuniqueness. We further provide the exact asymptotic behaviour of the… Expand
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