On oscillation and nonoscillation properties of Emden-Fowler difference equations

• Autorzy: Mariella Cecchi , Zuzana Došlá , Mauro Marini
• Języki publikacji: EN

Abstrakty

EN

A characterization of oscillation and nonoscillation of the Emden-Fowler difference equation $$ \Delta (a_n \left| {\Delta x_n } \right|^\alpha sgn\Delta x_n ) + b_n \left| {x_{n + 1} } \right|^\beta sgnx_{n + 1} = 0 $$ is given, jointly with some asymptotic properties. The problem of the coexistence of all possible types of nonoscillatory solutions is also considered and a comparison with recent analogous results, stated in the half-linear case, is made.

Słowa kluczowe

EN

Emden-Fowler type difference equation; Oscillation; Nonoscillation; Reciprocal principle

Kategorie tematyczne

• 39A10: Difference equations, additive

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 2
• Strony: 322-334

Daty

wydano

2009-06-01

online

2009-05-24

Twórcy

autor

Mariella Cecchi

• Department of Electronics and Telecommunications, University of Florence, Firenze, Italy

autor

Zuzana Došlá

• Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

autor

Mauro Marini

• Department of Electronics and Telecommunications, University of Florence, Firenze, Italy

Bibliografia

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• [2] Cecchi M., Došlá Z., Marini M., Nonoscillatory half-linear difference equations and recessive solutions, Adv. Difference Equ., 2005, 2, 193–204 http://dx.doi.org/10.1155/ADE.2005.193[Crossref]
• [3] Cecchi M., Došlá Z., Marini M., Vrkoč I., Summation inequalities and half-linear difference equations, J. Math. Anal. Appl., 2005, 302, 1–13 http://dx.doi.org/10.1016/j.jmaa.2004.08.005[Crossref]
• [4] Cecchi M., Došlá Z., Marini M., Vrkoč I., Asymptotic properties for half-linear difference equations, Math. Bohem., 2006, 131, 347–363
• [5] Cecchi M., Došlá Z., Marini M., On the growth of nonoscillatory solutions for difference equations with deviating argument, Adv. Difference Equ., 2008, Article ID 505324, 15 pp.
• [6] Cecchi M., Došlá Z., Marini M., Intermediate solutions for nonlinear difference equations with p-Laplacian, Advanced Studies in Pure Mathematics, 2009, 53, 45–52
• [7] Huo H.F., Li W.T., Oscillation of certain two-dimensional nonlinear difference systems, Comput. Math. Appl., 2003, 45, 1221–1226 http://dx.doi.org/10.1016/S0898-1221(03)00089-0[Crossref]
• [8] Jiang J., Li X., Oscillation and nonoscillation of two-dimensional difference systems, J. Comput. Appl. Math., 2006, 188, 77–88 http://dx.doi.org/10.1016/j.cam.2005.03.054[Crossref]
• [9] Li W.T., Oscillation theorems for second-order nonlinear difference equations, Math. Comput. Modelling, 2000, 31, 71–79 http://dx.doi.org/10.1016/S0895-7177(00)00047-9[Crossref]
• [10] Li W.T., Classification schemes for nonoscillatory solutions of two-dimensional nonlinear difference systems, Comput. Math. Appl., 2001, 42, 341–355 http://dx.doi.org/10.1016/S0898-1221(01)00159-6[Crossref]
• [11] Wong P.J.Y., Agarwal R.P, Oscillation and monotone solutions of second order quasilinear difference equations, Funkcial. Ekvac., 1996, 39, 491–517
• [12] Zhang G., Cheng S.S., Gao Y., Classification schemes for positive solutions of a second-order nonlinear difference equation, J. Comput. Appl. Math., 1999, 101, 39–51 http://dx.doi.org/10.1016/S0377-0427(98)00189-7[Crossref]

Identyfikatory

DOI

10.2478/s11533-009-0014-7