摘要：In this paper, we obtain the existence and multiplicity of solutions for discrete Neumann boundary value problem with singular ϕ-Laplacian operator ∇ ( Δ u k 1 − κ ( Δ u k ) 2 ) + r k u k + f ( k , u k , Δ u k ) = 0 , 2 ≤ k ≤ N − 1 , Δ u 1 = 0 = Δ u N − 1 by using upper and lower solutions method and Brouwer degree theory, where κ > 0 is a constant, r = ( r 2 , … , r N − 1 ) ∈ R N − 2 , and f is a continuous function. We also give some examples to illustrate the main results. MSC:34B10, 34B18.
关键词：singular ϕ -Laplacian ; existence ; Neumann problem ; Brouwer degree ; upper and lower solutions
