Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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MULTIPLICITY RESULTS FOR THE WAVE SYSTEM USING THE LINKING THEOREM

  • Nam, Hyewon (Department of General Education Namseoul University)
  • Received : 2013.04.30
  • Accepted : 2013.06.15
  • Published : 2013.06.30
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Abstract

We investigate the existence of solutions of the one-dimensional wave system $$u_{tt}-u_{xx}+{\mu}g(u+v)=f(u+v)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\v_{tt}-v_{xx}+{\nu}g(u+v)=f(u+v)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ with Dirichlet boundary condition. We find them by applying linking inequlaities.

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References

  1. Q-heung Choi and Tacksun Jung, Innitely many solutions of a wave equation with jumping nonlinearity, J. Korean Math. Soc. 37 (2000), 943-956.
  2. Q.H. Choi and T. Jung, An application of a variational reduction method to a nonlinear wave equation, J. Differential Equations 117 (1995), 390-410. https://doi.org/10.1006/jdeq.1995.1058
  3. 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
  4. S. Li, A. Squlkin, Periodic solutions of an asymptotically linear wave equation, Nonlinear Anal. 1 (1993), 211-230.