the existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous neumann boundary conditions. using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous neumann boundary conditions, we obtain the result.

In this paper we solve two biharmonic problems over a square, B = (−1, 1) × (−1, 1). (1) The problem ∇4U = f , for which we determine a particular solution, U , given f , via use of Sinc convolution; and (2) The boundary value problem ∇4V = 0 for which we determine V given V = g and normal derivative Vn = h on ∂B, the boundary of B. The solution to this problem is carried out based on the identity

A factoring and block elimination method for the fast numerical solution of block five diagonal linear algebraic equations is described. Applications of the method are given for the numerical solution of several boundary-value problems involving the biharmonic operator. In particular, 22 eigenvalues and eigenfunctions of the clamped square plate are computed and sketched.