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Pré-Publication, Document De Travail Année : 2012

Quasilinear Lane-Emden equations with absorption and measure data

Résumé

We study the existence of solutions to the equation $-\Gd_pu+g(x,u)=\mu$ when $g(x,.)$ is a nondecreasing function and $\gm$ a measure. We characterize the good measures, i.e. the ones for which the problem as a renormalized solution. We study particularly the cases where $g(x,u)=\abs x^{\beta}\abs u^{q-1}u$ and $g(x,u)=\abs x^{\tau}\rm{sgn }(u)(e^{\tau\abs u^\lambda}-1)$. 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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Dates et versions

hal-00768950 , version 1 (26-12-2012)
hal-00768950 , version 2 (15-01-2013)

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Marie-Françoise Bidaut-Véron, Hung Nguyen Quoc, Laurent Veron. Quasilinear Lane-Emden equations with absorption and measure data. 2012. ⟨hal-00768950v1⟩
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