Previous |  Up |  Next

Article

Keywords:
oscillation; nonlinear difference equation; Riccati transformation
Summary:
By means of Riccati transformation techniques, we establish some new oscillation criteria for second-order nonlinear difference equation which are sharp.
References:
[1] R. P.  Agarwal: Difference Equations and Inequalities, Theory, Methods and Applications. Second Edition. Marcel Dekker, New York, 2000. MR 1740241
[2] R. P.  Agarwal and P. J. Y.  Wong: Advanced Topics in Difference Equations. Kluwer Academic Publishers, Dordrecht, 1997. MR 1447437
[3] S. S.  Cheng: Hille-Wintner type comparison theorems for nonlinear difference equations. Funkc. Ekvacioj 37 (1994), 531–535. MR 1311559 | Zbl 0820.39003
[4] H. J.  Li and S. S.  Cheng: Asymptotically monotone solutions of a nonlinear difference equation. Tamkang J.  Math. 24 (1993), 269–282. MR 1246320
[5] W. T.  Li: Oscillation theorems for second-order nonlinear difference equations. Math. Comp. Modelling 31 (2000), 71–79. DOI 10.1016/S0895-7177(00)00047-9 | MR 1751841 | Zbl 1042.39516
[6] W. T.  Li and S. S. Cheng: Oscillation criteria for a nonlinear difference equation. Comput. Math. Appl. 36 (1998), 87–94. DOI 10.1016/S0898-1221(98)00185-0 | MR 1653847
[7] B.  Liu and S. S.  Cheng: Positive solutions of second order nonlinear difference equations. J.  Math. Anal. Appl. 204 (1996), 482–493. DOI 10.1006/jmaa.1996.0450 | MR 1421461
[8] Z. R.  Liu, W. D.  Chen and Y. H. Yu: Oscillation criteria for second-order nonlinear difference equations. Kyungpook Math.  J. 39 (1999), 127–132. MR 1698681
[9] M.  Peng, Q.  Xu, L.  Huang and W. G.  Ge: Asymptotic and oscillatory behavior of solutions of certain second-order nonlinear difference equations. Comp. Math. Appl. 37 (1999), 9–18. DOI 10.1016/S0898-1221(99)00041-3 | MR 1674415
[10] M.  Peng, W. G.  Ge and Q.  Xu: New criteria for the oscillation and existence of monotone solutions of second-order nonlinear difference equations. Appl. Math. Comp. 114 (2000), 103–114. DOI 10.1016/S0096-3003(99)00091-0 | MR 1775126
[11] Ch. G.  Philos: Oscillation theorems for linear differential equation of second order. Arch. Math. 53 (1989), 481–492. DOI 10.1007/BF01324723 | MR 1019162
[12] Z.  Szafranski and B.  Szmanda: Oscillation theorems for some nonlinear difference equations. Appl. Math. Comp. 83 (1997), 43–52. DOI 10.1016/S0096-3003(96)00045-8 | MR 1433167
[13] E.  Thandapani, I.  Gyori and B. S.  Lalli: An application of discrete inequality to second order nonlinear oscillation. J.  Math. Anal. Appl. 186 (1994), 200–208. DOI 10.1006/jmaa.1994.1294 | MR 1290652
[14] P. J. Y.  Wong and R. P.  Agarwal: Oscillation theorems for certain second order nonlinear difference equations. J.  Math. Anal. Appl. 204 (1996), 813–829. DOI 10.1006/jmaa.1996.0469 | MR 1422774
[15] P. J. Y.  Wong and R. P.  Agarwal: Oscillation and monotone solutions of second order quasilinear difference equations. Funkc. Ekvacioj 39 (1996), 491–517. MR 1433914
[16] B. G.  Zhang and G. D.  Chen: Oscillation of certain second order nonlinear difference equations. J.  Math. Anal. Appl. 199 (1996), 872–841. MR 1386608
[17] Z.  Zhang and P.  Bi: Oscillation of second order nonlinear difference equation with continuous variable. J.  Math. Anal. Appl. 255 (2001), 349–357. DOI 10.1006/jmaa.2000.7271 | MR 1813826
[18] A. B.  Mingarelli: Volterra Stieltjes integral equations and generalized ordianry differential expressions. Lecture Notes in Math., Vol.  989, 1983. MR 0706255
[19] G.  Zhang and S. S.  Cheng: A necessary and sufficient oscillation condition for the discrete Euler equation. PanAmerican Math.  J. 9 (1999), 29–34. MR 1724529
Partner of
EuDML logo