Large solutions for an elliptic system of quasilinear equations

@inproceedings{GarcaMelin2008LargeSF,
  title={Large solutions for an elliptic system of quasilinear equations},
  author={Jorge Garc{\'i}a-Meli{\'a}n},
  year={2008}
}
In this paper we consider the quasilinear elliptic system Δpu=uavb, Δpv=ucve in a smooth bounded domain Ω⊂RN, with the boundary conditions u=v=+∞ on ∂Ω. The operator Δp stands for the p-Laplacian defined by Δpu=div(|∇u|p−2∇u), p>1, and the exponents verify a,e>p−1, b,c>0 and (a−p+1)(e−p+1)⩾bc. We analyze positive solutions in both components, providing necessary and sufficient conditions for existence. We also prove uniqueness of positive solutions in the case (a−p+1)(e−p+1)>bc and obtain the… CONTINUE READING

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VIEW 5 EXCERPTS
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References

Publications referenced by this paper.
SHOWING 1-10 OF 49 REFERENCES

A remark on uniqueness of large solutions for elliptic systems of competitive type

J. Garćıa-Melián
  • J. Math. Anal. Appl. 331
  • 2007
VIEW 1 EXCERPT

Existence and uniqueness of positive solutions to the boundary blow-up problem for an elliptic system

H. Li, M. Wang
  • J. Diff. Eqns. 234
  • 2007
VIEW 1 EXCERPT

J

J. Garćıa-Melián, R. Letelier-Albornoz
  • Sabina de Lis, The solvability of an elliptic system under a singular boundary condition, Proc. Roy. Soc. Edinburgh 136
  • 2006
VIEW 1 EXCERPT

Nonlinear problems with singular boundary conditions arising in population dynamics: a Karamata regular variation theory approach

F. Ĉırstea, V. Rǎdulescu
  • Asymptotic Anal. 46
  • 2006
VIEW 1 EXCERPT