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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
##### Keywords:
critical growth; positive solutions