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We show the existence of positive solutions of the periodic problem of the quasilinear difference equation $$textstylebegin{cases} -nabla[phi(Delta u_{k})]+q_{k}u_{k}=lambda g_{k}f(u_{k}),quad kinmathbb {T}, u_{0}=u_{T}, qquad u_{1}=u_{T + 1}, end{cases} $$where (mathbb{T}={1, 2,ldots,T}) with integer (Tgeq2), (phi (s)=s/{sqrt{1-s^{2}}}), (boldsymbol{q}=(q_{1},ldots,q_{T})inmathbb{R}^{T}), (q_{k}geq0) for all (kinmathbb{T}) and (q_{k_{0}}u003e0) for some (k_{0}in mathbb{T}), (boldsymbol{g}=(g_{1},ldots,g_{T})inmathbb{R}^{T}) changes the sign on (mathbb{T}), f is a continuous function, and (lambdainmathbb {R}) is a parameter. The proofs of the main results are based upon bifurcation techniques.

Positive solutions of the periodic problems for quasilinear difference equation with sign-changing weight