Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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NONTRIVIAL SOLUTION FOR THE BIHARMONIC BOUNDARY VALUE PROBLEM WITH SOME NONLINEAR TERM

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2013.02.06
  • Accepted : 2013.06.10
  • Published : 2013.06.30
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Abstract

We investigate the existence of weak solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We get a theorem which shows the existence of nontrivial solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We obtain this result by reducing the biharmonic problem with nonlinear term to the biharmonic problem with bounded nonlinear term and then approaching the variational method and using the mountain pass geometry for the reduced biharmonic problem with bounded nonlinear term.

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References

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  1. Fourth order elliptic boundary value problem with nonlinear term decaying at the origin vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-432
  2. AN APPLICATION OF LINKING THEOREM TO FOURTH ORDER ELLIPTIC BOUNDARY VALUE PROBLEM WITH FULLY NONLINEAR TERM vol.22, pp.2, 2013, https://doi.org/10.11568/kjm.2014.22.2.355