서강대학교

초록/요약

In this thesis, we deal with inverse problems, resonance problems and anti-minimum principle involving the discrete p-Laplacian with potential terms and weight function h which is the discrete analogue of the p-Laplacian on Riemannian manifolds. We investigate indefinite eigenvalue problems and the properties of eigenfunctions corresponding to the smallest indefinite eigenvalue for the discrete p-Laplacian with potential terms under the Dirichlet boundary condition. Then we discuss relations between the first indefinite eigenvalue and the Poisson Equation with Dirichlet boundary conditions with the operators. Moreover, we present some properties of the first indefinite eigenvalue and eigenfuction on the finite networks. We also prove the minimum principle, the comparison principle, the Dirichlet principle and the Dirichlet boundary value problems for the operator. Finally, we show the global uniqueness of the inverse conductivity and potential problems for the operator under suitable monotonicity conditions and we prove the resonance problems and anti-minimum principle.