  We establish uniqueness results for quasilinear elliptic problems through the
criterion recently provided in \cite{DFMST}. We apply it to generalized
$p$-Laplacian subhomogeneous problems that may admit multiple nontrivial
nonnegative solutions. Based on a generalized hidden convexity result, we show
that uniqueness holds among strongly positive solutions and nonnegative global
minimizers. Problems involving nonhomogeneous operators as the so-called
$(p,r)$-Laplacian are also treated.
