*Published Paper*

**Inserted:** 13 jul 2018

**Last Updated:** 13 jul 2018

**Journal:** Journal de Mathématiques Pures et Appliquées

**Year:** 2014

**Doi:** https://www.sciencedirect.com/science/article/pii/S0021782413001748

**Abstract:**

We study the existence of solutions to the equation $-\Delta_pu+g(x,u)=\mu$
when $g(x,.)$ is a nondecreasing function and $\mu$ a measure. We characterize the good measures, i.e. the ones for which the problem has a renormalized solution. We study particularly the cases where $g(x,u)=

x

^{-\beta}

u

^{q-1}u$ and $g(x,u)=\text{sign }(u)(e^{\tau

u

^\lambda} -1)$. The results state that a measure is good if it is absolutely continuous with respect to an appropriate Lorentz-Bessel capacities.

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