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Volume 14,     Number 2,     Summer 2006

 

OSCILLATION AND ASYMPTOTIC BEHAVIOR
OF A THIRD-ORDER NONLINEAR
DYNAMIC EQUATION
L. ERBE, A. PETERSON AND S. H. SAKER

Dedicated to Professors Jack W. Macki and James S. Muldowney

Abstract. In this paper we establish some new oscillation criteria for the third-order nonlinear dynamic equation
                               
on time scales, where γ ≥ 1 is a quotient of odd integers. Our results not only unify the oscillation theory for third-order nonlinear differential and difference equations but also are new for the q-difference equations and can be applied on different time scales. The results improve some of the main results in the literature in the case when γ = 1.

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© 2006, Canadian Applied Mathematics Quarterly (CAMQ)