Geodesic
Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 4, pp. 485-491.

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Let $p>1$, $q>p$, $\lambda >0$ and $s\in ]1,p[$. We study, for $s\rightarrow p^-$, the behavior of positive solutions of the problem $-\Delta_p u = \lambda u^{s-1}+u^{q-1}$ in $\Omega$, $u_{\mid\partial \Omega}=0$. In particular, we give a positive answer to an open question formulated in a recent paper of the first author.
Classification : 35J20, 35J25, 35J92
Keywords: elliptic boundary value problems; positive solutions; variational methods; asymptotic behavior; combined nonlinearities 
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     title = {Asymptotic behavior of positive solutions of a {Dirichlet} problem involving supercritical nonlinearities},
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Anello, Giovanni; Rao, Giuseppe. Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 4, pp. 485-491. http://geodesic.mathdoc.fr/item/CMUC_2013__54_4_a2/