International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 781-784

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

B. Smith

Department of Mathematics, Texas Southern University, Houston 77004, Texas, USA

Received 6 August 1985

Copyright © 1986 B. Smith. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, asymptotic properties of solutions ofΔ3Vn+Pn1Vn+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.