Spectra Of A Discrete Sturm-Liouville Problems With Eigenparameter-Dependent Boundary Conditions In Pontryagin Space

In the paper,we consider the second order discrete Sturm-Liouville problems-?(p(t)?u(t))+q(t)y(t)=?m(t)y(t),t?[1,T]Z,(a0?+b0)y(0)=(c0?+d0)?y(0),(a1?+b1)y(T+1)=(c1?+d1)?y(T+1),where ? is the forward difference operator satisfying ?y(t)=y(t+1)-y(t),? is the backward difference operator satisfying ?y(t)=y(t)-y(t-1),? is the spectrum parameter,p:[0,T]z?(0,+?),q:[1,T]z?R,m:[1,T]z?(0,+?),?0=a0d0-b0c0<0,?1=a1d1-b1c1<0.Different from the results of Gao and Ma[21],the operator corresponding to the problem here is not self-adjoint in the corresponding Hilbert space.According to the construction of the new Lagrange-type identites,the existence,simplicity and interlacing properties of real eigenvalues,nonreal eigenvalues and the oscillation properties of eigenfunctions are obtained in this paper.