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APPLICATIONS OF CRITICAL POINT THEOREMS TO NONLINEAR BEAM PROBLEMS

Choi, Q-Heung;Jin, Ying-Hua;Choi, Kyung-Pyo

  • Received : 2006.12.07
  • Accepted : 2007.01.22
  • Published : 2007.03.25

Abstract

Let L be the differential operator, Lu = $u_{tt}+u_{xxxx}$. We consider nonlinear beam equations, Lu + $bu^+$ = j, in H, where H is the Hilbert space spanned by eigenfunctions of L. We reveal the existence of multiple solutions of the nonlinear beam problems by critical point theorems.

Keywords

nonlinear beam problem;critical point theorem;eigenfunction

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Cited by

  1. Existence of infinitely many solutions of a beam equation with non-monotone nonlinearity vol.33, 2017, https://doi.org/10.1016/j.nonrwa.2016.06.010