JournalspmVol. 64 / No. 3DOI 10.4171/pm/1786

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