Positive solutions of semilinear equations in cones

@inproceedings{Egnell1992PositiveSO,
  title={Positive solutions of semilinear equations in cones},
  author={Henrik Egnell},
  year={1992}
}
In this paper we consider the problem of finding a positive solution of the equation Am + |jc|"M("+2+2l/'/(n_2) = 0 in a cone f , with zero boundary data. We are only interested in solutions that are regular at infinity (i.e. such that u(x) = o(|jc|2-") , as W 3 x -» oo). We will always assume that v > — 2. We show that the existence of a solution depends on the sign of v and also on the shape of the cone fe7. 

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