Critical elliptic equations via a dynamical systems approach. (May 2019) - Ai, Shangbing; Cowan, Craig
Abstract: In this work we consider the existence of positive solutions to various equations of the form − Δ u ( x ) = ( 1 + g ( | x |, u ) ) u ( x ) p in  B R, u = 0 on  ∂ B R, where B R is the open ball of radius R in R N centered at the origin and p = N + 2 N − 2 . We will generally assume g is nonnegative. Our approach will be to utilize some dynamical systems approaches.