Discrete third-order three-point boundary value problem

We are concerned with the discrete boundary value problemLx(t)≔Δ3x(t)=f(t,x(t+1)),t1⩽t⩽t3-1,x(t1)=0,αx(t2)-βΔx(t2)=0,γx(t3)+δΔ2x(t3)=0,and the eigenvalue problem Δ3x(t)=λf(t,x(t+1)) with the same boundary conditions where t1