Opuscula Math. 26, no. 2 (2006), 343-349

 
Opuscula Mathematica

Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)

Jarosław Mikołajski
Ewa Schmeidel

Abstract. Third order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscillation and boundedness. Especially the numbers of suitable types of solutions taken out from fundamental sets are presented. We give conditions under which the asymptotic properties considered are the same for the both equations.

Keywords: differential equation, recurrence, linear, third order, oscillatory solution, bounded solution.

Mathematics Subject Classification: 34A05, 34C10, 34C11, 39A10.

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Cite this article as:
Jarosław Mikołajski, Ewa Schmeidel, Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients), Opuscula Math. 26, no. 2 (2006), 343-349

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