In this paper we prove the global solvability of a class of fourth-order nonlinear boundary value problems that govern the deformation of a Hollomon’s power-law plastic beam subject to an axial compression and nonlinear lateral constrains. For certain ranges of the acting axial compression force, the solvability of the equations follows from the monotonicity of the fourth order nonlinear differential operator. Beyond these ranges the monotonicity of the operator is lost. It is shown that, in this case, the global solvability may be generated by the lower order nonlinear terms of the equations for a certain type of constrains.
Applied Mathematical Sciences
Elgindi, M.B.M. and Wei, Dongming, "On the Global Solvability of a Class of Fourth-Order Nonlinear Boundary Value Problems" (2012). Mathematics Faculty Publications. Paper 23.: 5981