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

### P. Habets

Université Catholique de Louvain, Belgium### Margarita Ramalho

Universidade de Lisboa, Portugal

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## Abstract

We consider the nonlinear fourth order beam equation

$u^{\iv}=f(t,u,u''),$

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

$u^{\iv}-cu''+du=g(t,u,u''),$

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

## Cite this article

P. Habets, Margarita Ramalho, A monotone method for fourth order boundary value problems involving a factorizable linear operator. Port. Math. 64 (2007), no. 3, pp. 255–279

DOI 10.4171/PM/1786