Abstract
We study the existence of positive solutions to quasilinear elliptic equations of the type −Δpu=σuq+μinRn,in the sub-natural growth case 0<q<p−1, where Δpu=∇⋅(|∇u|p−2∇u) is the p-Laplacian with 1<p<n, and σ and μ are nonnegative Radon measures on Rn. 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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