A monotone method for fourth order boundary value problems involving a factorizable linear operator

Abstract

We consider the nonlinear fourth order beam equation

with boundary conditions corresponding to the periodic or the hinged beam problem. In presence of upper and lower solutions, we consider a monotone method to obtain solutions. The main idea is to write the equation in the form

where $c$, $d$ are adequate constants, and use maximum principles and a suitable decomposition of the operator appearing in the left-hand side.