Nonlinear equations with natural growth terms and measure data ∗

  title={Nonlinear equations with natural growth terms and measure data ∗},
  author={Alessio Porretta},
We consider a class of nonlinear elliptic equations containing a pLaplacian type operator, lower order terms having natural growth with respect to the gradient, and bounded measures as data. The model example is the equation −∆p(u) + g(u)|∇u| = μ in a bounded set Ω ⊂ R , coupled with a Dirichlet boundary condition. We provide a review of the results recently obtained in the absorption case (when g(s)s ≥ 0) and prove a new existence result without any sign condition on g, assuming only that g… CONTINUE READING

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