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Existence and multiple solutions for a second-order difference boundary value problem via critical point theory. (English) Zbl 1112.39008

This paper deals with the existence and multiplicity of solutions to a second-order difference boundary value problem

Δ(p k-1 Δx k-1 )+q k x k +f(k,x k )=0,k[1,N],
x 0 =x N ,p 0 Δx 0 =p N Δx N ·

Under some appropriate assumptions, the authors give some sufficient conditions on the existence and multiplicity of solutions for the above mentioned difference boundary value problem. The main tools used here are the classical variational methods and a variant version of a theorem due to D. C. Clark [Math. J., Indiana Univ. 22, 65–74 (1972; Zbl 0228.58006)].

39A12Discrete version of topics in analysis
39A10Additive difference equations