International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 2, Pages 257-261
doi:10.1155/S0161171297000343
On the global solvability of a class of fourth-order nonlinear boundary value problems
Department of Mathematics, University of Wisconsin - Eau Claire, Eau Claire 54702, Wisconsin, USA
Received 16 May 1995
Copyright © 1997 M. B. M. Elgindi and Zhengyuan Guan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.