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

M. B.M. Elgindi, Dongming Wei

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)5981-5992
Number of pages12
JournalApplied Mathematical Sciences
Volume6
Issue number117-120
Publication statusPublished - Oct 16 2012

Keywords

  • Coercivity
  • Fourth-order nonlinear boundary value problems
  • Global solvability
  • Leray-schauder fixed point theorem
  • Monotone operator

ASJC Scopus subject areas

  • Applied Mathematics

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