“…Recently, much attention has been also paid to certain fourth-order elliptic boundary value problems in multiple dimensions (cf. [7,[14][15][16][17]21]). In this paper, we focus on the following two-dimensional fourth-order nonlinear elliptic boundary value problem: ∆(k(x, y)∆u) = f (x, y, u, ∆u), (x, y) ∈ Ω , u(x, y) = g(x, y), ∆u(x, y) = g * (x, y), (x, y) ∈ ∂Ω , (1.2) where Ω is a rectangular domain or a union of rectangular domains, and ∆ is the Laplacian operator.…”