Uniqueness of positive solutions to a class of quasilinear differential equations (Q1296443)

The authors investigate the boundary value problem \[ (|u'|^{p-2}u')'+{n-1\over r}|u'|^{p-2}u'+u^{\alpha}+u^{\beta}=0,\qquad u'(0)=u(R)=0, \] for \(0<r<R\) and \(1<p<n\), \(\beta<np/(n-p)-1\), \(\alpha\in(\beta,(1+\beta)p/n+p-1)\). The uniqueness of positive solutions is studied. The main result consists in showing that the above problem possesses exactly one nontrivial positive solution.