Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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MOUNTAIN PASS GEOMETRY APPLIED TO THE NONLINEAR MIXED TYPE ELLIPTIC PROBLEM

  • Jung Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi Q-Heung (Department of Mathematics Education Inha University)
  • Received : 2009.09.23
  • Published : 2009.12.30
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Abstract

We show the existence of at least one nontrivial solution of the homogeneous mixed type nonlinear elliptic problem. Here mixed type nonlinearity means that the nonlinear part contain the jumping nonlinearity and the critical growth nonlinearity. We first investigate the sub-level sets of the corresponding functional in the Soboles space and the linking inequalities of the functional on the sub-level sets. We next investigate that the functional I satisfies the mountain pass geometry in the critical point theory. We obtain the result by the mountain pass method, the critical point theory and variational method.

Keywords

References

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