Eigenvalue comparisons for a class of boundary value problems of discrete beam equation

We study the structure of eigenvalues of a class of boundary value problems of fourth order difference equationΔ4yi+bi+2yi+2=λai+2yi+2,-1⩽i⩽n-2,Δy0=Δ3y-1=Δyn=Δ3yn-1=0.The monotone behavior of the eigenvalues as the sequences {ai}i=1n and {bi}i=1n change is obtained in this paper.