Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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SOLVABILITY FOR A CLASS OF THE SYSTEM OF THE NONLINEAR SUSPENSION BRIDGE EQUATIONS

  • Jung, Tack-Sun (Department of Mathematics, Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education, Inha University)
  • Received : 2008.09.27
  • Accepted : 2009.03.07
  • Published : 2009.03.25
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Abstract

We show the existence of the nontrivial periodic solution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between two sublevel sets. Since the functional is strongly indefinite, we use the linking theorem for the strongly indefinite functional and the notion of the suitable version of the Palais-Smale condition.

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References

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