Quasilinear and Hessian Lane-Emden Type Systems with Measure Data

  • Marie-Françoise Bidaut-Véron
  • Quoc-Hung Nguyen
  • Laurent VéronEmail author


We study nonlinear systems of the form \(-{\Delta }_{p}u=v^{q_{1}}+\mu , -{\Delta }_{p}v=u^{q_{2}}+\eta \) and \(F_{k}[-u]=v^{s_{1}}+\mu , F_{k}[-v]=u^{s_{2}}+\eta \) in a bounded domain Ω or in \(\mathbb {R}^{N}\) where μ and η are nonnegative Radon measures, Δp and Fk are respectively the p-Laplacian and the k-Hessian operators and q1, q2, s1 and s2 positive numbers. We give necessary and sufficient conditions for existence expressed in terms of Riesz or Bessel capacities.


p-Laplacian k-Hessian Bessel and Riesz capacities Measures Maximal functions 

Mathematics Subject Classification 2010

35J70 35J60 45G15 31C15 


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© Springer Nature B.V. 2018

Authors and Affiliations

  • Marie-Françoise Bidaut-Véron
    • 1
  • Quoc-Hung Nguyen
    • 2
  • Laurent Véron
    • 2
    Email author
  1. 1.Scuola Normale SuperioreCentro Ennio de GiorgiPisaItaly
  2. 2.Laboratoire de Mathématiques et Physique ThéoriqueUniversité François RabelaisToursFrance

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