Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities. (English) Zbl 1313.35077
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.
MSC:
35J20 | Variational methods for second-order elliptic equations |
35J25 | Boundary value problems for second-order elliptic equations |