Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

APPLICATIONS OF CRITICAL POINT THEOREMS TO NONLINEAR BEAM PROBLEMS

  • Received : 2006.12.07
  • Accepted : 2007.01.22
  • Published : 2007.03.25
Download PDF
⟨ Previous Next ⟩

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

References

  1. Q.H. Choi, T. Jung, P.J. McKenna, The study of a nonlinear suspension bridge equation by a variational reduction method. Appl. Anal. 50 (1993), 71-90. https://doi.org/10.1080/00036819308840185
  2. H. Hofer, On strongly indefinite functionals with applications. Trans. Amer. Math. Soc. 275 (1983), 185-214. https://doi.org/10.1090/S0002-9947-1983-0678344-2
  3. L. Humphreys, Numerical and theoretical results on large amplitude periodic so­lutions of a suspension bridge equation. ph.D. thesis, University of Connecticut (1994).
  4. S. Li, A. Squlkin, Periodic solutions of an asymptotically linear wave equation. Nonlinear Analysis, 1 (1993), 211-230.
  5. J.Q. Liu, Free vibrations for an asymmetric beam equation. Nonlinear Analysis, 51 (2002), 487-497. https://doi.org/10.1016/S0362-546X(01)00841-0
  6. P.J. McKenna, W. Walter, Nonlinear Oscillations in a Suspension Bridge. Arch. Rational Mech. Anal. 98 (1987), 167-177. https://doi.org/10.1007/BF00251232
  7. A.M. Micheletti, C. Saccon, Multiple nontrivial solutions for a floating beam via critical point theory. J. Differential Equations, 170 (2001), 157-179. https://doi.org/10.1006/jdeq.2000.3820

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