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http://dx.doi.org/10.4134/BKMS.2015.52.5.1517

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.5, 2015 , pp. 1517-1533 More about this Journal
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.
Keywords
p-Laplacian difference equation; discrete p-Laplacian; discrete boundary value problems;
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