  We study the existence of positive solutions to quasilinear elliptic
equations of the type \[ -\Delta_{p} u = \sigma u^{q} + \mu \quad \text{in} \
\mathbb{R}^{n}, \] in the sub-natural growth case $0 < q < p - 1$, where
$\Delta_{p}u = \nabla \cdot ( |\nabla u|^{p - 2} \nabla u )$ is the
$p$-Laplacian with $1 < p < n$, and $\sigma$ and $\mu$ are nonnegative Radon
measures on $\mathbb{R}^{n}$. We construct minimal generalized solutions under
certain generalized energy conditions on $\sigma$ and $\mu$. To prove this, we
give new estimates for interaction between measures. We also construct
solutions to equations with several sub-natural growth terms using the same
methods.
