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A telescoping principle for oscillation of the second order half-linear dynamic equations on time scales

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Tatra Mountains Mathematical Publications
Differential and Difference Equations and Applications 2008

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[1] AGARWAL, R. P.: Difference Equations and Inequalities: Theory, Methods, and Applications (2nd ed.), Pure Appl. Math., Vol. 228, Marcel Dekker, New York, 2000.10.1201/9781420027020Search in Google Scholar

[2] AGARWAL, R. P.-BOHNER, M.-GRACE, S. R.-O’REGAN, D.: Discrete Oscillation Theory. Hindawi Publ. Co., New York, 2005.10.1155/9789775945198Search in Google Scholar

[3] BOHNER, M.: Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions, J. Math. Anal. Appl. 199 (1996), 804-826.10.1006/jmaa.1996.0177Search in Google Scholar

[4] BOHNER, M.-PETERSON, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkh¨auser, Boston, 2001.10.1007/978-1-4612-0201-1Search in Google Scholar

[5] BOHNER, M.-PETERSON, A.: Advances in Dynamic Equations on Time Scales. Birkh¨auser, Boston, 2003.10.1007/978-0-8176-8230-9Search in Google Scholar

[6] DOˇSL´Y, O.: Qualitative theory of half-linear second order differential equations, Math. Bohem. 127 (2002), 181-195.10.21136/MB.2002.134170Search in Google Scholar

[7] DOˇSL´Y, O.-ˇREH´AK, P.: Nonoscilation criteria for second order half-linear difference equations, Comput. Math. Appl. 42 (2001), 453-464.10.1016/S0898-1221(01)00169-9Search in Google Scholar

[8] DOˇSL´Y, O.-ˇREH´AK, P.: Half-linear Differential Equations. North-Holland Math. Stud., Vol. 202, Elsevier, Amsterdam, 2005.Search in Google Scholar

[9] ERBE, L. H.-PETERSON, A. C.: Some recent results in linear and nonlinear oscillation, Dynam. Systems Appl. 13 (2004), 381-395.Search in Google Scholar

[10] ERBE, L. H.-KONG, L.-KONG, Q.: A telescoping principle for oscillation of second order differential equations on time scale, Rocky Mountain J. Math. 36 (2006), 149-181.10.1216/rmjm/1181069493Search in Google Scholar

[11] HARTMAN, P.: Ordinary Differential Equations. John Wiley, New York, 1973.Search in Google Scholar

[12] KONG, Q.-ZETTL, A.: Interval oscillation conditions for difference equations, SIAM J. Math. Anal. 26 (1995), 1047-1060.10.1137/S0036141093251286Search in Google Scholar

[13] KWONG, M. K.-ZETTL, A.: Integral inequalities and second order linear oscillation, J. Differential Equations 45 (1982), 16-23.10.1016/0022-0396(82)90052-3Search in Google Scholar

[14] ˇREH´AK, P.: Oscillation criteria for second order half-linear difference equations, J. Difference Equ. Appl. 7 (2001), 483-505.10.1080/10236190108808284Search in Google Scholar

[15] ˇREH´AK, P.: Half-linear dynamic equations on time scales: IVP and oscillatory properties, Nonlinear Funct. Anal. Appl. 7 (2002), 361-404.Search in Google Scholar

[16] ˇREH´AK, P.: Comparison theorems and strong oscillation in the half-linear discrete oscillation theory, Rocky Mountain J. Math. 33 (2003), 333-352.Search in Google Scholar

[17] STURM, J. C. F.: M´emoire sur le ´equations differentielles lin´earies du second ordre, J. Math. Pures Appl. (9) 1 (1836), 106-186.Search in Google Scholar

[18] SWANSON, C. A.: Comparison and Oscillation Theory of Linear Differential Equations. Academic Press, New York, 1968.Search in Google Scholar

ISSN:
1210-3195
Language:
English
Publication timeframe:
3 times per year
Journal Subjects:
Mathematics, General Mathematics