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

Title & Authors
MULTIPLE SOLUTIONS TO DISCRETE BOUNDARY VALUE PROBLEMS FOR THE p-LAPLACIAN WITH POTENTIAL TERMS ON FINITE GRAPHS
CHUNG, SOON-YEONG; PARK, JEA-HYUN;

Abstract
In this paper, we prove the existence of at least three nontrivial solutions to nonlinear discrete boundary value problems $\small{\{^{-{\Delta}_{p,{\omega}}u(x)+V(x){\mid}u(x){\mid}^{q-2}u(x)=f(x,u(x)),x{\in}S,}_{u(x)=0,\;x{\in}{\partial}S}}$, involving the discrete p-Laplacian on simple, nite and connected graphs $\small{\bar{S}(S{\cup}{\partial}S,E)}$ with weight $\small{{\omega}}$, where 1 < q < p < $\small{{\infty}}$. 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;
Language
English
Cited by
1.
Existence and multiplicity results for boundary value problems connected with the discrete p ( · ) − Laplacian on weighted finite graphs, Applied Mathematics and Computation, 2016, 290, 376
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