Comparison theorems for the oscillation of higher order neutral delay diference equations

• Autorzy: Zhou Y. , Zhang B. G.
• Języki publikacji: EN

Abstrakty

EN

We obtain a necessary and sufficient condition for the oscillation of the higher order neutral delay difference equation m(Xn -pnxn-r) + f(n, xg1(n),xg2(n), ...,xg1(n))=0 where m > 1 is an odd integer. As some application of this result, we estabilish three comparison theorems for the oscillation of the above equation.

Słowa kluczowe

EN

oscillation; comparison theorems; neutral differential equation

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 3
• Strony: 545--555
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Zhou Y.

• Department of Mathematics, Xiangtan University, Hunan 411105, P. R. China

autor

Zhang B. G.

• Department of Applied Mathematics, Ocean University of Qingdao, Qingdao, 266003, P. R. China

Bibliografia

• [1] R. P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992.
• [2] R. P. Agarwal and P. J. Y. Wong, Advanced Topics in Difference Equations, Kluwer Academic Publishers, Dordrecht, 1997.
• [3] L. H. Erbe, Q. Kong and B. G. Zhang, Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York, 1995.
• [4] K. Gopalsamy, B. S. Lalli and B. G. Zhang, Oscillation in odd order neutral differential equations, Czech. Math. J. 42 (1992), 313-323.
• [5] P. J. Y. Wong and R. P. Agarwal, Comparison theorems for the oscillation of higher order difference equations with deviating arguments, Math. Comput. Modelling 24 (1996), 39-48.
• [6] J. Yan, Comparison theorems for the oscillation of higher order neutral equations and applications, Scientia Sinica, Ser A12 (1990), 1256-1266.
• [7] B. G. Zhang, J. S. Yu and Ζ. C. Wang, Oscillations of higher order neutral differential equations, Rocky Mountain J. Math. 25 (1995), 557-568.
• [8] B. G. Zhang and B. Yang, Oscillation in higher order nonlinear difference equations (in Chinese), Chinese Ann. Math. 20 (1999), 71-80.
• [9] G. Zhang and Y. Gao, Positive solutions of higher order nonlinear difference equations (in Chinese), J. Systems Sci. Math. Sci. 19 (1999), 157-161.
• [10] Yong Zhou, Oscillation of neutral difference equations, Kyungpook Math. J. 39 (1999), 283-291.
• [11] Yong Zhou and B. G. Zhang, The semicycles of solutions of neutral difference equations, Appi. Math. Lett. 13 (2000), 59-66.
• [12] Yong Zhou and B. G. Zhang, Classification and existences of nonoscillatory solutions of second-order neutral delay difference equation, J. Anal. Appl. 20 (2001), 223-234.