zbMATH — the first resource for mathematics

Asymptotics for elliptic equations involving critical growth. (English) Zbl 0685.35013
Partial differential equations and the calculus of variations. Essays in Honor of Ennio De Giorgi, 149-192 (1989).
[For the entire collection see Zbl 0671.00007.]
The author considers the problem \[ -\Delta u_{\epsilon}=\lambda u_{\epsilon}+3u_{\epsilon}^{5-\epsilon},\quad u_{\epsilon}>0 \] with 0 boundary data in a ball of \(R^ 3.\)
The asymptotic behaviour of \(u_{\epsilon}\) as \(\epsilon\) \(\to 0\) is studied for \(0\leq \lambda <\pi^ 2/4\) by methods of PDE.
Reviewer: M.Biroli

35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations