Quasilinear and Hessian Type Equations with Exponential Reaction and Measure Data |
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Authors: | Quoc-Hung Nguyen Laurent Véron |
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Institution: | 1. Laboratoire de Mathématiques et Physique Théorique, Université Fran?ois Rabelais, Tours, France
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Abstract: | We prove existence results concerning equations of the type \({-\Delta_pu=P(u)+\mu}\) for p > 1 and F k ?u] = P(u) + μ with \({1 \leqq k < \frac{N}{2}}\) in a bounded domain Ω or the whole \({\mathbb{R}^N}\) , where μ is a positive Radon measure and \({P(u)\sim e^{au^\beta}}\) with a > 0 and \({\beta \geqq 1}\) . Sufficient conditions for existence are expressed in terms of the fractional maximal potential of μ. Two-sided estimates on the solutions are obtained in terms of some precise Wolff potentials of μ. Necessary conditions are obtained in terms of Orlicz capacities. We also establish existence results for a general Wolff potential equation under the form \({u={\bf W}_{\alpha, p}^RP(u)]+f}\) in \({\mathbb{R}^N}\) , where \({0 < R \leqq \infty}\) and f is a positive integrable function. |
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