The Dirichlet problem for sublinear elliptic equations with source

We present a necessary and sufficient condition on nonnegative Radon measures $μ$ and $ν$ for the existence of a positive continuous solution of the Dirichlet problem for the sublinear elliptic equation $-Δu=μu^q+ν$ with prescribed nonnegative continuous boundary data in a general domain. Moreover, two-sided pointwise estimates of Brezis-Kamin type for positive bounded solutions and the uniqueness of a positive continuous $L^q$-solution are investigated.

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