On the global solvability of a class of fourth-order nonlinear boundary value problems

Abstract

This paper is concerned with the global solvability of a class of fourth-order nonlinear boundary value problems that govern the deformation of an elastic beam which is acted upon by axial compression, lateral forces and is in contact with a semi-infinite medium acting as a foundation For certain ranges of the acting axial compression force, the solvability of the equations follows from the coercivity of their linear parts. Beyond these ranges this coercivity is lost. It is shown here that the coercivity which ensures the global solvability can be generated by the nonlinear parts of the equations for a certain type of foundation.