Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems, III

@inproceedings{Byeon2000EffectOS,
  title={Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems, III},
  author={Jaeyoung Byeon},
  year={2000}
}
We consider the problem:Δu+hu+f(u)=0inΩRu=0on∂ΩRu>0inΩR, where ΩR≡{x∈RN ∣ R−1<|x|<R+1} and the function f and the constant h satisfy suitable assumptions. This problem is invariant under the orthogonal coordinate transformations, in other words, O(N)-symmetric. Let G be an infinite closed subgroup of O(N). We investigate how the symmetry subgroup G affects the structure of positive solutions. Considering a natural G group action on a sphere SN−1, we give a partial order on the space of G−orbits… CONTINUE READING

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