Quasilinear and Hessian type equations with exponential reaction and measure data

Abstract

We prove existence results concerning equations of the type $-{\Delta }_{p}u=P(u)+\mu$ for $p>1$ and $F_k[-u]=P(u)+\mu$ with $1\le k<\frac{N}{2}$ in a bounded domain $\Omega$ or the whole ${\mathbb{R}}^N$, where $\mu$ is a positive Radon measure and $P(u)\sim e^{a{u}^{\beta }}$ with $a>0$ and $\beta \ge 1$. Sufficient conditions for existence are expressed in terms of the fractional maximal potential of $\mu$. Two-sided estimates on the solutions are obtained in terms of some precise Wolff potentials of $\mu$. Necessary conditions are obtained in terms of Orlicz capacities. We also establish existence results for a general Wolff potential equation under the form $u={\mathbf{W}}_{\alpha ,p}^R[P(u)]+f$ in ${\mathbb{R}}^N$, where $0

à paraître à Arch. Rat. Mech. Anal

References in corpus (2)

• Elliptic Equations Involving Meausres
• Some Liouville Theorems for the p-Laplacian

Cited by in corpus (1)

• A characterization of fast decaying solutions for quasilinear and Wolff type systems with singular coefficients