The variational framework corresponding to a class of the second-order nonlinear difference equations(Pλ) with the parameters was obtained.It was proved that the solutions of the problem(Pλ) were equivalent to the critical points of the functional(Jλ) in Banach space H.By appling critical point theorem in the setting of finite dimensional Banach space

the multiplicity of solutions for(Pλ) was investigated.It is proved that

for every λ belonging to a well defined open interval

the problem(Pλ) has at least three distinct positive solutions.