Existence of minimal solutions to quasilinear elliptic equations with several sub-natural growth terms

We study the existence of positive solutions to quasilinear elliptic equations of the type $-Δ_{p} u = σu^{q} + μ\quad \text{in} \ \mathbb{R}^{n},$ in the sub-natural growth case $0 < q < p - 1$, where $Δ_{p}u = \nabla \cdot ( |\nabla u|^{p - 2} \nabla u )$ is the $p$-Laplacian with $1 < p < n$, and $σ$ and $μ$ are nonnegative Radon measures on $\mathbb{R}^{n}$. We construct minimal generalized solutions under certain generalized energy conditions on $σ$ and $μ$. 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.

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