# MULTIPLE SOLUTIONS TO DISCRETE BOUNDARY VALUE PROBLEMS FOR THE p-LAPLACIAN WITH POTENTIAL TERMS ON FINITE GRAPHS

• CHUNG, SOON-YEONG (DEPARTMENT OF MATHEMATICS AND PROGRAM OF INTEGRATED BIOTECHNOLOGY SOGANG UNIVERSITY) ;
• PARK, JEA-HYUN (DEPARTMENT OF MATHEMATICS KUNSAN NATIONAL UNIVERSITY)
• Received : 2014.08.11
• Published : 2015.09.30

#### Abstract

In this paper, we prove the existence of at least three nontrivial solutions to nonlinear discrete boundary value problems $$\{^{-{\Delta}_{p,{\omega}}u(x)+V(x){\mid}u(x){\mid}^{q-2}u(x)=f(x,u(x)),x{\in}S,}_{u(x)=0,\;x{\in}{\partial}S}$$, involving the discrete p-Laplacian on simple, nite and connected graphs $\bar{S}(S{\cup}{\partial}S,E)$ with weight ${\omega}$, where 1 < q < p < ${\infty}$. The approach is based on a suitable combine of variational and truncations methods.

#### Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

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