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

作者：Chung Soon Yeong^*; Park Jea Hyun

来源：Bulletin of the Korean Mathematical Society, 2015, 52(5): 1517-1533.

DOI：10.4134/BKMS.2015.52.5.1517

• p-Laplacian difference equation
• discrete p-Laplacian
• discrete
• boundary value problems

In this paper, we prove the existence of at least three nontrivial solutions to nonlinear discrete boundary value problems
{ -Delta(p,w)u(x)+V(x)vertical bar u(x))vertical bar(q-2)u(x) = f(x,u(x)) x is an element of S,
u(x) = 0, x is an element of partial derivative S,
involving the discrete p-Laplacian on simple, finite and connected graphs (S) over bar (S boolean OR partial derivative S, E) with weight omega where 1 < q < p < infinity. The approach is based on a suitable combine of variational and truncations methods.

• 出版日期2015