Disconjugacy of a third-order linear difference equation.

摘要

We consider the third-order linear difference equation ;We discretize the ordinary differential equation ;Next we present the important concepts of generalized zeros, disconjugacy, and (1,2)- and (2,1)-pairs of zeros. We prove several technical lemmas about these concepts. We also discuss several summation formulas.;We then prove several important theorems on (1,2)- and (2,1)-disconjugacy. Then we show the equivalence of disconjugacy and Polya factorization for ;Next we consider the (2,1)-boundary value problem and (2,2)-disfocality for the difference equation ;Finally, we give several examples of constant coefficient equations of