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Growth and oscillation properties of solutions of a fourth order linear difference equation

Published online by Cambridge University Press:  17 February 2009

John W. Hooker  and
William T. Patula
William T. Patula
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, U.S.A.
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Abstract

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For the fourth-order linear difference equation Δ4un−2 = bn un, with bn > 0 for all n, generalized zeros are defined, following Hartman [5], and two theorems are proved concerning separation of zeros of linearly independent solutions. Some preliminary results deal with non-oscillation and asymptotic behavior of solutions of this equation for various types of initial conditions. Finally, recessive solutions are defined, and results are obtained analogous to known results for recessive solutions of second-order difference equations.

Type
Research Article
Information
The ANZIAM Journal , Volume 26 , Issue 3 , January 1985 , pp. 310 - 328
Copyright
Copyright © Australian Mathematical Society 1985

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