Remarks on nonlinear equations with measures

We study the Dirichlet boundary value problem for equations with absorption of the form $-Δu+g\circ u=μ$ in a bounded domain $Ω\subset R^N$ where $g$ is a continuous odd monotone increasing function. Under some additional assumptions on $g$, we present necessary and sufficient conditions for existence when $μ$ is a finite measure. We also discuss the notion of solution when the measure $μ$ is positive and blows up on a compact subset of $\Gw$.

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