A bifurcation diagram of solutions to an elliptic equation with exponential nonlinearity in higher dimensions

  title={A bifurcation diagram of solutions to an elliptic equation with exponential nonlinearity in higher dimensions},
  author={Hiroaki Kikuchi and Juncheng Wei},
  journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
  pages={101 - 122}
We consider the following semilinear elliptic equation: where B 1 is the unit ball in ℝ d , d ≥ 3, λ > 0 and p > 0. Firstly, following Merle and Peletier, we show that there exists an eigenvalue λ p,∞ such that (*) has a solution (λ p,∞ ,W p ) satisfying lim |x|→0 Wp (x) = ∞. Secondly, we study a bifurcation diagram of regular solutions to (*). It follows from the result of Dancer that (*) has an unbounded bifurcation branch of regular solutions that emanates from (λ, u) = (0, 0). Here, using… 
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