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Summary: A FOURTH-ORDER NONLINEAR DIFFERENCE EQUATION
DOUGLAS R. ANDERSON1
Abstract. We are concerned with solutions of the fourth-order nonlinear difference equa-
tion 2
pn2
yn - (qnyn+1) = f(n, yn+2), where pn > 0, qn 0. We define F+
and
F-
solutions for a certain functional operator F, prove the existence of these solutions,
and verify asymptotic properties of these solutions under the assumption that f satisfies
yf(n, y) < 0.
Dedicated to Allan Peterson on the occasion of his 60th birthday.
1. Introduction
We will be concerned with the fourth-order nonlinear difference equation
(1) 2
pn2
yn - (qnyn+1) = f(n, yn+2)
for n N, where f : (N, R) R and
(2) pn > 0, qn 0.
Here is the forward difference operator defined by yn = yn+1-yn. Solutions y = {yn}
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