Elliptic equations with nearly critical growth (Q1110721)

The author studies what happens to the solution of the boundary value problem \[ (1)\quad -\Delta u=u^ p\quad u>0\quad in\quad \Omega \in R^ N;\quad u=0\quad on\quad \partial \Omega \] if p approaches the critical Sobolev exponent \(p=(N+2)/(N-2)\) (if \(p\geq (N+2)/(N-2)\), the problem (1) has no solutions) and \(\Omega =B_ R=\{x\in R^ N:\) \(x<R\}\). He uses ODE arguments to obtain precise asymptotic estimates as \(p\to (N+2)/(N-2)=0\).