### Abstract

This paper concerns the existence and uniqueness of equilibrium states of a beam- column with hinged ends which is acted upon by axial compression and lateral forces and is in contact with a semi-infinite medium acting as a foundation. The problem is formulated as a fourth- order nonlinear boundary value problem in which the source of the nonlinearity comes from the lateral constraint (the foundation). Treating the equation of equilibrium as a nonlinear eigenvalue problem we prove the existence of a pair of eigenvalue/eigenfunction for each arbitrary prescribed energy level. Treating the equilibrium equation as a nonlinear boundary value problem we prove the existence and uniqueness of solution for a certain range of the acting axial compression force.

Original language | English |
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Pages (from-to) | 193-198 |

Number of pages | 6 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 16 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1993 |

Externally published | Yes |

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### Keywords

- beam-column
- elastic beam
- Existence of equilibrium states
- fourth-order nonlinear boundary value problem
- nonlinear eigenvalue problems
- variational methods

### ASJC Scopus subject areas

- Mathematics (miscellaneous)