Positive and compacton-type solutions for a quasilinear two-point boundary value problem (Q2352194)

The paper is concerned with the following boundary value problem \[ -\bigl( |u'|^{p-2} u' \bigr)' = \lambda u^{s-1} - \mu u^{r-1} + u^{q-1}, \;\, t \in (0,1); \;\;\, u(0)=u(1)=0 \] with parameters \(\lambda, \mu >0\) and \(1< r<s <p <q\). The authors study the existence of positive solutions satisfying some special properties.