호남수학학술지 (Honam Mathematical Journal)

  • 제29권1호
  • /
  • Pages.19-40
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  • 2007
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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APPLICATIONS OF CRITICAL POINT THEOREMS TO NONLINEAR BEAM PROBLEMS

  • 투고 : 2006.12.07
  • 심사 : 2007.01.22
  • 발행 : 2007.03.25
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초록

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.

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참고문헌

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  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

피인용 문헌

  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