Ground States and Dirichlet Problems for — Δu = f(u) in R2

@inproceedings{Atkinson1986GroundSA,
  title={Ground States and Dirichlet Problems for — Δu = f(u) in R2},
  author={Frederick V. Atkinson and L. A. Peletier},
  year={1986}
}
In an earlier paper [1] we considered the existence of solutions of the problem $$egin{gathered} - elta u = feft( u ight),u > 0,peratorname{in} {peratorname{R} ^N} fill ueft( x ight) o 0peratorname{as} |x| o nfty fill nd{gathered} $$ (I) in which f(u) is to be positive for large u, but not for all u > O. Such solutions are sometimes called “ground states”, a term borrowed from the physical context (nonlinear field equations) in which Problem I arises. Following in part the approach of… CONTINUE READING

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