Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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EXISTENCE OF THE SOLUTIONS FOR THE ELLIPTIC PROBLEM WITH NONLINEAR TERM DECAYING AT THE ORIGIN

  • Choi, Q-Heung (Department of Mathematics Education Inha University) ;
  • Jung, Tacksun (Department of Mathematics Kunsan National University)
  • Received : 2012.11.10
  • Accepted : 2012.12.15
  • Published : 2012.12.30
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Abstract

We consider the multiplicity of the solutions for the elliptic boundary value problem with $C^1$ nonlinear term decaying at the origin. We get a theorem which shows the existence of the nontrivial solution for the elliptic problem with $C^1$ nonlinear term decaying at the origin. We obtain this result by reducing the elliptic problem with the $C^1$ nonlinear term to the el-liptic problem with bounded nonlinear term and then approaching the variational method and using the mountain pass geometry for the reduced the elliptic problem with bounded nonlinear term.

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References

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