# Article

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Keywords:
elliptic boundary value problems; positive solutions; variational methods; asymptotic behavior; combined nonlinearities
Summary:
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.
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