A monotone method for fourth order boundary value problems involving a factorizable linear operator
P. Habets
Université Catholique de Louvain, BelgiumMargarita Ramalho
Universidade de Lisboa, Portugal

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 , 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