Existence and location results for the bending of an elastic beam

Abstract

In this paper it is obtained an existence and location result for some fourth order fully nonlinear equation with Lidstone boundary conditions. The nonlinearity verifies a Nagumo-type condition without assumptions of bound type and monotonicity restrictions. The existence of at least a solution lying between a pair of well ordered lower and upper solutions is obtained using a priori estimates, lower and upper solutions method and degree theory.