Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions

  title={Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions},
  author={Ciprian G. Gal and andMahamadi Warma},
Given a bounded domain Ω ⊂ R with a Lipschitz boundary ∂Ω and p, q ∈ (1, +∞), we consider the quasilinear elliptic equation −Δ pu+α1(u) = f inΩ complemented with the generalizedWentzell-Robin type boundary conditions of the form b(x)|∇u|p−2∂nu− ρb(x)Δ q,Γu + α2(u) = g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems… CONTINUE READING

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