THE ROLE OF LOWER AND UPPER SOLUTIONS IN THE GENERALIZATION OF LIDSTONE PROBLEMS

Abstract

In this the authors consider a nonlinear fourth order fully equation coupled with the Lidstone boundary conditions, We discuss how di erent de nitions of lower and upper solutions can generalize existence and location results for boundary value problems with Lidstone boundary data. In addition, it is replaced the usual bilateral Nagumo condition by a one-sided condition, allowing the nonlinearity to be unbounded: An example will show that this unilateral condition generalizes the usual one and stress the potentialities of the new de nitions.