Gro Hovhannisyan, Oliver Ruff
Abstract:
We consider the Cauchy problem for second and third order linear differential
equations with constant complex coefficients. We describe necessary and
sufficient conditions on the data for the existence of oscillatory solutions.
It is known that in the case of real coefficients the oscillatory behavior
of solutions does not depend on initial values, but we show that this is no
longer true in the complex case: hence in practice it is possible to control
oscillatory behavior by varying the initial conditions.
Our Proofs are based on asymptotic analysis of the zeros of solutions,
represented as linear combinations of exponential functions.
Submitted May 6, 2015. Published June 24, 2015.
Math Subject Classifications: 34C10.
Key Words: Linear ordinary differential equation; oscillation;
initial value problem; characteristic polynomial; characteristic roots.
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Gro Hovhannisyan Kent State University at Stark 6000 Frank Ave. NW Canton, OH 44720-7599, USA email: ghovhann@kent.edu | |
Oliver Ruff Kent State University at Stark 6000 Frank Ave. NW Canton, OH 44720-7599, USA email: oruff@kent.edu |
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