Unilateral global structure for discrete Dirichlet problem with Minkowski-curvature operator

In this paper, we are concerned with the unilateral global bifurcation results for the Minkowski-curvature discrete problem {−∇[ϕ(Δu(t))]=λa(t)u(t)+f(t,u(t),λ),t∈[1,T]Z,u(0)=u(T+1)=0,where λ∈R is a parameter, a:[1,T]Z→(0,∞),f∈C([1,T]Z×R2,R), Δ is the forward difference operator with Δu(t)=u(t+1)−u(t) and ∇ is the backward difference operator with ∇u(t)=u(t)−u(t−1), ϕ(s)=s1−s2 is a ϕ-Laplacian operator. We shall show that there are two distinct unbounded continua C+ and C−, consisting of the bifurcation branch C if f is not necessarily differentiable at the origin with respect to u.