  In this paper, we consider a nonlinear beam equation with the p-biharmonic
operator, where $1 < p < \infty$. Using a change of variable, we transform the
problem into a system of differential equations and prove the existence,
uniqueness and regularity of the weak solution by applying the Lax-Milgram
theorem and classical results of functional analysis. We investigate the
discrete formulation for that system and, with the aid of the Brouwer theorem,
we show that the problem has a discrete solution. The uniqueness and stability
of the discrete solution are obtained through classical methods. After
establishing the order of convergence, we apply the mixed finite element method
to obtain an algebraic system of equations. Finally, we implement the
computational codes in Matlab software and perform the comparison between
theory and simulations.
