A three dimensional Steklov eigenvalue problem with exponential nonlinearity on the boundary

We investigate the existence of pairs (λ,u)(λ,u), with λ>0λ>0 and uu a harmonic function in a bounded domain Ω⊂R3Ω⊂R3, such that the nonlinear boundary condition ∂νu=λμsinhu holds on ∂Ω∂Ω, where μμ is a non negative weight function. This type of exponential boundary condition arises in corrosion modeling (Butler–Volmer condition).