Elliptic equations with nearly critical growth. (English) Zbl 0657.35058

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 \(p\to (N+2)/(N-2)=0\).
Reviewer: J.H.Tian


35J65 Nonlinear boundary value problems for linear elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
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