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

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  • M. B. M. Elgindi
  • Zhengyuan Guan

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.

Suggested Citation

  • M. B. M. Elgindi & Zhengyuan Guan, 1997. "On the global solvability of a class of fourth-order nonlinear boundary value problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-5, January.
    • Handle: RePEc:hin:jijmms:320518
    DOI: 10.1155/S0161171297000343
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    Cited by:

    1. Ravi P. Agarwal & Petio S. Kelevedjiev, 2020. "On the Solvability of Fourth-Order Two-Point Boundary Value Problems," Mathematics, MDPI, vol. 8(4), pages 1-19, April.

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