Oscillatory properties of second order half-linear difference equations

Czechoslovak Mathematical Journal

Volumn 51, Issue 2, 2001, Pages 303-321

  Řehák, Pavel ^a  

^a MASARYK UNIVERSITY   (Czech Republic)

Author keywords

Half linear difference equation; Oscillation criteria; Picone identity; Reid Roundabout Theorem

Indexed keywords

EID: 23044529828     PISSN: 00114642     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1013790713905     Document Type: Article

References (16)

1. R. P. Agarwal: Difference equations and inequalities, theory, methods, and applications, the second edition. Pure and Appl. Math. M. Dekker, New York-Basel-Hong Kong, 2000.
2. C. D. Ahlbrandt and A. C. Peterson: Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations. Kluwer Academic Publishers, Boston, 1996.
3. O. Došlý: Oscillation criteria for higher order Sturm-Liouville difference equations. J. Differ. Equations Appl. 4 (1998), 425-450.
4. O. Došlý: Oscillation criteria for half-linear second order differential equations. Hiroshima Math. J. 28 (1998), 507-521.
5. O. Došlý: A remark on conjugacy of half-linear second order differential equations. Math. Slovaca 50 (2000), 67-79.
6. O. Došlý and P. Řehák: Nonoscillation criteria for second order half-linear difference equations. Comput. Math. Appl. In press.
7. Á. Elbert: A half-linear second order differential equations. Colloq. Math. Soc. János Bolayi 30 (1979), 158-180.
8. Á. Elbert and T. Kusano: Principal solutions of nonoscillatory half-linear differential equations. Adv. Math. Sci. Appl. (Tokyo) 8 (1998), 745-759.
9. J. Jaroš and T. Kusano: A Picone type identity for second order half-linear differential equations. Acta Math. Univ. Comenian. (M.S.) 68 (1999), 137-151.
10. W. G. Kelley and A. Peterson: Difference Equations: An Introduction with Applications. Acad. Press, San Diego, 1991.
11. J. D. Mirzov: On some analogs of Sturm's and Kneser's theorems for nonlinear systems. J. Math. Anal. Appl. 3 (1976), 418-425.
12. J. D. Mirzov: Principial and nonprincipial solutions of a nonoscillatory system. Tbiliss. Cos. Univ. Inst. Prikl. Mat. Trudy 31 (1988), 100-117.
13. P. Řehák. Half-linear discrete oscillation theory. In: Proceedings of 6th Colloquium on the qualitative theory of DE, Szeged 1999, http://www.math.u-szeged.hu/ejqtde/index.html. EJQTDE, Szeged, 2000, pp. 1-14.
14. P. Řehák: Half-linear dynamic equations on time scales: IVP and oscillatory properties. Submitted.
15. P. Řehák. Hartman-Wintner type lemma, oscillation and conjugacy criteria for half-linear difference equations. J. Math. Anal. Appl. 252 (2000), 813-827.
16. P. Řehák. Oscillation criteria for second order half-linear difference equations. J. Differ. Equations Appl. In press.