The <i>p</i>-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 p-Schrödinger operator Lp,ω and solve the following p-Schrödinger equation: Lp,ωu = −Δ_p,ωu + q_|u|p_−2_u = f on networks. To show the uniqueness of solutions of the p-Schrödinger equation, we first solve the eigenvalue problem for the p-Schrödinger operator and obtain some properties of the smallest eigenvalue and its corresponding eigenfunction of the p-Schrödinger operator.

Cite this article

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

DOI 10.2977/PRIMS/1241553123