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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

MSC:

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

Citations:

Zbl 0671.00007