Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity

@article{Ghergu2018ExactBA,
  title={Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity},
  author={Marius Ghergu and Sunghan Kim and Henrik Shahgholian},
  journal={Advances in Nonlinear Analysis},
  year={2018},
  volume={8},
  pages={995 - 1003}
}
Abstract We study the semilinear elliptic equation - Δ u = u α | log u | β   in B 1 ∖ { 0 } , -\Delta u=u^{\alpha}\lvert\log u|^{\beta}\quad\text{in }B_{1}\setminus\{0\}, where B 1 ⊂ ℝ n {B_{1}\subset{\mathbb{R}}^{n}} , with n ≥ 3 {n\geq 3} , n n - 2 < α < n + 2 n - 2 {\frac{n}{n-2}<\alpha<\frac{n+2}{n-2}} and - ∞ < β < ∞ {-\infty<\beta<\infty} . Our main result establishes that the nonnegative solution u ∈ C 2 ⁢ ( B 1 ∖ { 0 } ) {u\in C^{2}(B_{1}\setminus\{0\})} of the above equation either has… 
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