Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ONE-DIMENSIONAL JUMPING PROBLEM INVOLVING p-LAPLACIAN

  • Jung, Tacksun (Department of Mathematics, Kunsan National University) ;
  • Choi, Q-Heing (Department of Mathematics Education, Inha University)
  • Received : 2018.08.31
  • Accepted : 2018.12.06
  • Published : 2018.12.30
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Abstract

We get one theorem which shows existence of solutions for one-dimensional jumping problem involving p-Laplacian and Dirichlet boundary condition. This theorem is that there exists at least one solution when nonlinearities crossing finite number of eigenvalues, exactly one solutions and no solution depending on the source term. We obtain these results by the eigenvalues and the corresponding normalized eigenfunctions of the p-Laplacian eigenvalue problem when 1 < p < ${\infty}$, variational reduction method and Leray-Schauder degree theory when $2{\leq}$ p < ${\infty}$.

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References

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