대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제26권4호
  • /
  • Pages.591-601
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  • 2011
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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THE p-LAPLACIAN OPERATORS WITH POTENTIAL TERMS

  • 투고 : 2010.06.23
  • 발행 : 2011.10.31
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초록

In this paper, we deal with the discrete p-Laplacian operators with a potential term having the smallest nonnegative eigenvalue. Such operators are classified as its smallest eigenvalue is positive or zero. We discuss differences between them such as an existence of solutions of p-Laplacian equations on networks and properties of the energy functional. Also, we give some examples of Poisson equations which suggest a difference between linear types and nonlinear types. Finally, we study characteristics of the set of a potential those involving operator has the smallest positive eigenvalue.

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참고문헌

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  2. S.-Y. Chung and J. H. Kim, The p-Laplacian and the uniqueness of inverse problems on nonlinear networks, preprint.
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  7. D. Ingerman and J. A. Morrow, On a characterization of the kernel of the Dirichlet-to- Neumann map for a planar region, SIAM J. Math. Anal. 29 (1998), no. 1, 106-115. https://doi.org/10.1137/S0036141096300483
  8. J.-H. Park, J.-H. Kim, and S.-Y. Chung, The p-Schrodinger equations on finite networks, Publ. Res. Inst. Math. Sci. 45 (2009), 363-381. https://doi.org/10.2977/prims/1241553123