International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 781-784
doi:10.1155/S0161171286000947

Quasi-adjoint third order difference equations: Oscillatory and asymptotic behavior

Abstract

In this paper, asymptotic properties of solutions ofΔ3Vn+Pn−1Vn+1=0          (E+)are investigated via the quasi-adjoint equationΔ3Un+PnUn+2=0.             (E−)A necessary and sufficient condition for the existence of oscillatory solutions of (E+) is given. An example showing that it is possible for (E+) to have only nonoscillatory solutions is also given.