Hardy inequality on time scales and its application to half-linear dynamic equations

Archives of Inequalities and Applications

Volumn 3, Issue 5, 2005, Pages 495-507

  Řehák, Pavel ^a  

^a MATHEMATICAL INSTITUTE   (Czech Republic)

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EID: 33645070204     PISSN: 15426149     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. R. P. Agarwal, M. Bohner, and P. Řehák, Half-linear dynamic equations, Nonlinear Analysis and Applications: to V. Lakshmikantham on his 80th birthday. Vol. 1, 2, Kluwer Academic, Dordrecht, 2003, pp. 1-57.
2. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser Boston, Massachusetts, 2001.
3. M. Bohner and A. Peterson (eds.), Advances in Dynamic Equations on Time Scales, Birkhäuser Boston, Massachusetts, 2003.
4. M. Bohner and S. H. Saker, Oscillation of second order nonlinear dynamic equations on time scales, Rocky Mountain J. Math. 34 (2004), no. 4, 1239-1254.
5. S. S. Cheng and R. F. Lu, A generalization of the discrete Hardy's inequality, Tamkang J. Math. 24 (1993), no. 4, 469-475.
6. O. Došlý, Oscillation criteria for half-linear second order differential equations, Hiroshima Math. J. 28 (1998), no. 3, 507-521.
7. O. Došlý and P. Řehák, Nonoscillation criteria for half-linear second-order difference equations, Comput. Math. Appl. 42 (2001), no. 3-5, 453-464.
8. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd ed., 1st. paperback ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1988.
9. S. Hilger, Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. dissertation, Universität of Würzburg, Würzburg, 1988.
10. R. Hilscher, A time scales version of a Wirtinger-type inequality and applications, J. Comput. Appl. Math. 141 (2002), no. 1-2, 219-226.
11. A. Kufner, Hardy's inequality and related topics, Function Spaces, Differential Operators and Nonlinear Analysis (Paseky nad Jizerou, 1995) (J. Rákosník, ed.), Prometheus, Prague, 1996, pp. 89-99.
12. A. Kufner and L.-E. Persson, Weighted Inequalities of Hardy Type, World Scientific, New Jersey, 2003.
13. D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, Mathematics and Its Applications (East European Series), vol. 53, Kluwer Academic, Dordrecht, 1991.
14. B. Opic and A. Kufner, Hardy-Type Inequalities, Pitman Research Notes in Mathematics Series, vol. 219, Longman Scientific & Technical, Harlow, 1990.
15. J. E. Pečarić and E. R. Love, Still more generalizations of Hardy's inequality, J. Austral. Math. Soc. Ser. A 59 (1995), no. 2, 214-224.
16. P. Řehák, Half-linear dynamic equations on time scales: IVP and oscillatory properties, Nonlinear Funct. Anal. Appl. 7 (2002), no. 3, 361-403.
17. _, On certain comparison theorems for half-linear dynamic equations on time scales, Abstr. Appl. Anal. 2004 (2004), no. 7, 551-565.
18. B. Yang, Z. Zeng, and L. Debnath, On new generalizations of Hardy's integral inequality, J. Math. Anal. Appl. 217 (1998), no. 1, 321-327.