JournalspmVol. 64, No. 3pp. 255–279

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

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Abstract

We consider the nonlinear fourth order beam equation

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

where cc, dd 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