The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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VARIATIONAL APPROACH AND THE NUMBER OF THE NONTRIVIAL PERIODIC SOLUTIONS FOR A CLASS OF THE SYSTEM OF THE NONTRIVIAL SUSPENSION BRIDGE EQUATIONS

  • Jung, Tack-Sun (DEPARTMENT OF MATHEMATICS, KUNSAN NATIONAL UNIVERSITY) ;
  • Choi, Q-Heung (DEPARTMENT OF MATHEMATICS EDUCATION, INHA UNIVERSITY)
  • Published : 2009.05.31
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Abstract

We investigate the multiplicity of the nontrivial periodic solutions for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We show that the system has at least two nontrivial periodic solutions by the abstract version of the critical point theory on the manifold with boundary. We investigate the geometry of the sublevel sets of the corresponding functional of the system and the topology of the sublevel sets. Since the functional is strongly indefinite, we use the notion of the suitable version of the Palais-Smale condition.

Keywords

References

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