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)

• Autorzy: Mikołajski J. , Schmeidel E.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

differential equation; recurrence; linear; third order; oscillatory solution; bounded solution

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2006
• Tom: Vol. 26, no. 2
• Strony: 343--349
• Opis fizyczny: Bibliogr. 20 poz., tab.

Twórcy

autor

Mikołajski J.

autor

Schmeidel E.

• Poznań University of Technology, Institute of Mathematics, Faculty of Electrical Engineering, ul. Piotrowo 3a, 60-965 Poznań, Poland,

Bibliografia

• [1] Agarwal R.P., Difference Equations and Inequalities. Theory, Methods and Applications, Marcel Dekker, New York, 2000 (2nd ed.).
• [2] Andruch-Sobiło A., Migda M., Bounded solutions of third order nonlinear difference equations, Rocky Mountain Journal of Mathematics 36 (2006) 1, 23-24.
• [3] Dosla Z., Kobza A., Global asymptotic properties of third order difference equations, Computers and Mathematics with Applications 48 (2004) 1-2, 191-200.
• [4] Elaydi S.N., An Introduction to Difference Equations, Springer, 1996.
• [5] Graef J.R., Thandapani E., Oscillatory and asymptotic behavior of solutions of third order delay difference equations, Funkcialaj Ekvacioj 42 (1999) 3, 355-369.
• [6] Kelley W.G., Peterson A. C, Difference Equations, an Introduction with Applications, Academic Press, 1991.
• [7] Kobza A., Property A for third order difference equations, Studies of the University of Zilina, Mathematical Series 17 (2003), 109-14.
• [8] Koźniewska I., Równania rekurencyjne, PWN, Warszawa, 1972 (in Polish)
• [9] Migda M., Schmeidel E., Drozdowicz A., Nonoscillation results for some third order nonlinear difference equation, Folia Facultatis Scientiarium Naturalium Universitatis Masarykianae Brunensis Mathematica 13 (2003), 185-192.
• [10] Mikołajski J., Schmeidel E., Comparison of boundedness of solutions of third order linear differential and recurrence equations with constant coefficients (submitted).
• [11] Mikołajski J., Schmeidel J., Porównanie rozwiązań równań różniczkowych i równań rekurencyjnych o tym samym równaniu charakterystycznym (in Polish, submitted).
• [12] Mostowski A., Stark A., Elementy algebry wyższej, PWN, Warszawa, 1968 (in Polish).
• [13] Palczewski A., Równania różniczkowe zwyczajne, WNT, Warszawa, 1999 (in Polish).
• [14] Popenda J., Schmeidel E., Nonoscillatory solutions of third order difference equations, Portugaliae Mathematica 49 (1992), 233-239.
• [15] Saker S.H., Oscillation of third-order difference equations, Portugaliae Mathematica 61 (2004) 3, 249-257.
• [16] Smith B., Oscillatory and asymptotic behavior in certain third order difference equations, Rocky Mountain Journal of Mathematics 17 (1987) 3, 597-606.
• [17] Smith B., Oscillation and no oscillation theorems for third order quasi-adjoint difference equations, Portugaliae Mathematica 45 (1988) 3, 229-243.
• [18] Smith B., Taylor W. E., Oscillatory and asymptotic behavior of certain fourth order difference equations, Rocky Mountain Journal of Mathematics 16 (1986) 2, 403-406.
• [19] Stiepanow W. W., Równania różniczkowe, PWN, Warszawa, 1964 (in Polish).
• [20] Thandapani E., Mahalingam K., Oscillatory properties of third order neutral delay difference equations, Demonstratio Mathematica 35 (2002), 325-337.