The -Schrödinger Equations on Finite Networks

  • Jea-Hyun Park

    Sogang University, Seoul, South Korea
  • Jong-Ho Kim

    National Institute for Mathematical Sciences, Daejeon, South Korea
  • Soon-Yeong Chung

    Sogang University, Seoul, South Korea


We introduce the discrete -Schrödinger operator and solve the following -Schrödinger equation:

on networks. To show the uniqueness of solutions of the -Schrödinger equation, we first solve the eigenvalue problem for the -Schrödinger operator and obtain some properties of the smallest eigenvalue and its corresponding eigenfunction of the -Schrödinger operator.

Cite this article

Jea-Hyun Park, Jong-Ho Kim, Soon-Yeong Chung, The -Schrödinger Equations on Finite Networks. Publ. Res. Inst. Math. Sci. 45 (2009), no. 2, pp. 363–381

DOI 10.2977/PRIMS/1241553123