Positive solutions for discrete boundary value problems involving the p-Laplacian with potential terms

Authors:
Jea-Hyun Park;Soon-Yeong Chung
Affiliations:
Institute of Mathematical Science, Ewha Womans University, Seoul, Republic of Korea;Department of Mathematics and Program of Integrated Biotechnology, Sogang University, Seoul, Republic of Korea
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 6
Cited 0

The Dirichlet to Neumann map for a resistor network

SIAM Journal on Applied Mathematics
Discrete Green's functions

Journal of Combinatorial Theory Series A
Solving Dirichlet and Poisson problems on graphs by means of equilibrium measures

European Journal of Combinatorics
On the discrete version of Picone's identity

Discrete Applied Mathematics
Multiple solutions for a discrete boundary value problem involving the p-Laplacian

Computers & Mathematics with Applications
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing

IEEE Transactions on Image Processing

Quantified Score

Hi-index	0.09

Visualization

Abstract

In this paper, we discuss the existence and the uniqueness of discrete boundary value problems involving the p-Laplacian with potential terms. To this end, we deal with the strong comparison principle and the Dirichlet principle for the p-Laplacian with potential terms on weighted graphs with boundary. Moreover, we provide a lower bound of the potential terms which guarantees the existence of solutions of the boundary value problem for the operator. Finally, we also discuss inverse conductivity and potential problems for the operator.