Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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MULTIPLE SOLUTIONS RESULT FOR THE MIXED TYPE NONLINEAR ELLIPTIC PROBLEM

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2011.10.23
  • Accepted : 2011.11.25
  • Published : 2011.12.30
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Abstract

We obtain a theorem that shows the existence of multiple solutions for the mixed type nonlinear elliptic equation with Dirichlet boundary condition. Here the nonlinear part contain the jumping nonlinearity and the subcritical growth nonlinearity. We first show the existence of a positive solution and next find the second nontrivial solution by applying the variational method and the mountain pass method in the critical point theory. By investigating that the functional I satisfies the mountain pass geometry we show the existence of at least two nontrivial solutions for the equation.

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References

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  2. EXISTENCE OF THE SOLUTIONS FOR THE ELLIPTIC PROBLEM WITH NONLINEAR TERM DECAYING AT THE ORIGIN vol.20, pp.4, 2012, https://doi.org/10.11568/kjm.2012.20.4.533
  3. EXISTENCE OF SOLUTIONS FOR ELLIPTIC SYSTEM WITH NONLINEARITIES UNDER THE DIRICHLET BOUNDARY CONDITION vol.23, pp.4, 2011, https://doi.org/10.11568/kjm.2015.23.4.591