A nonlinear boundary problem involving the p-bilaplacian operator

∆p := ∆(|∆u|p−2∆u) is the operator of fourth order, so-called the p-biharmonic (or p-bilaplacian) operator. For p = 2, the linear operator ∆2 = ∆2 = ∆ · ∆ is the iterated Laplacian that to a multiplicative positive constant appears often in the equations of Navier-Stokes as being a viscosity coefficient, and its reciprocal operator noted (∆2)−1 is the celebrated Green’s operator (see [8]). Existence results for nonlinear boundary problem have only been considered in recent years. For the second-order p-Laplacian with nonlinear boundary conditions of different type, see [5], see also [3]. For a fourth-order elliptic equation with the ordinary boundary conditions, we cite [2] and with nonlinear boundary conditions, see [4].