Disconjugacy and C-disfocality of second-order self-adjoint difference equation

The disconjugacy and the C-disfocality of the second-order self-adjoint difference equationLu(t)≡Δ[p(t)Δu(t−1)]+q(t)u(t)=0, are discussed in this paper, where p(t) is nonzero with same sign on N(a + 1, b + 2) and q(t) is real valued on N(a + 1, b + 1). Some sufficient conditions are obtained explicitly in terms of coefficients, which can be easily verified. These results generalize some known ones in the literature.