American Institute of Mathematical Sciences

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2003, 2003(Special): 423-431. doi: 10.3934/proc.2003.2003.423

Oscillation of an Euler-Cauchy dynamic equation

S. Huff 1, , G. Olumolode 1, , N. Pennington 1, and  A. Peterson 1,

1. 

University of Nebraska-Lincoln, Lincoln, NE 65888-0323, United States, United States, United States, United States

Received  September 2002 Published  April 2003

The Euler-Cauchy differential equation and difference equation are well known. Here we study a more general Euler-Cauchy dynamic equation. For this more general equation when we have complex roots of the corresponding characteristic equation we for the first time write solutions of this dynamic equation in terms of a generalized exponential function and generalized sine and cosine functions. This result is even new in the difference equation case. We then spend most of our time studying the oscillation properties of the Euler-Cauchy dynamic equation. Several oscillation results are given and an open problem is posed.
Keywords: time scale, Euler¨CCauchy dynamic equation, oscillation..
Mathematics Subject Classification: Primary: 39A10; Secondary: 34B1.
Citation: S. Huff, G. Olumolode, N. Pennington, A. Peterson. Oscillation of an Euler-Cauchy dynamic equation. Conference Publications, 2003, 2003 (Special) : 423-431. doi: 10.3934/proc.2003.2003.423
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