Non-oscillation of a class of third order nonhomogeneous difference equations

摘要

Sufficient conditions, in terms of coefficient functions, are obtained for non-oscillation of a class of linear third order non-homogeneous difference equations of the form y(n + 3) + a(n)y(n + 2) + b(n)y(n + 1) + c(n)y(n) = f (n); n ≥ 0; ?~3y(n - 1) + a(n)?~2y(n - 1) + b(n)Dy(n) + c(n)y(n) = f (n - 1); n ≥ 1 and D(p(n - 1)?~2y(n - 1)) + q(n)Dy(n) + r(n)y(n) = f (n - 1); n ≥ 1; where c(n) - 0 and p(n) > 0. The available methods, usually used for the study of difference equations, are developed appropriately for this purpose.