Asymptotic behaviour of semi-canonical third-order functional difference equations. Issue 4 (3rd April 2022) - Srinivasan, R.
Abstract : Asymptotic properties of solutions of the third-order functional difference equation 1 D z ( n ) + f ( n ) z ( σ ( n ) ) = 0, where D z ( n ) = Δ ( b ( n ) Δ ( a ( n ) Δ z ( n ) ) ) is a semi-canonical difference operator is studied. The main idea is to transform the semi-canonical operator into the canonical form, which simplifies the examination of the asymptotic properties of solutions. Examples are provided to illustrate the significance of the main results.