On the Global Solvability of a Class of Fourth- Order Nonlinear Boundary Value Problems
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Date
2012
Authors
Elgindi, Mohamed B. M.
Wei, Dongming
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematics Faculty Publications
Abstract
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.
Description
Keywords
Global solvability, fourth-order nonlinear boundary value problems, monotone operator, Leray-Schauder fixed point theorem, coercivity
Citation
Elgindi, M.B.M. and Wei, Dongming; 2012; On the Global Solvability of a Class of Fourth- Order Nonlinear Boundary Value Problems; Mathematics Faculty Publications; http://nur.nu.edu.kz/handle/123456789/1924