Rocky Mountain Journal of Mathematics
- Rocky Mountain J. Math.
- Volume 36, Number 1 (2006), 149-181.
A Telescoping Principle for Oscillation of Second Order Differential Equations on a Time Scale
Lynn Erbe, Lingju Kong, and Qingkai Kong
Full-text: Open access
Article information
Source
Rocky Mountain J. Math., Volume 36, Number 1 (2006), 149-181.
Dates
First available in Project Euclid: 5 June 2007
Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181069493
Digital Object Identifier
doi:10.1216/rmjm/1181069493
Mathematical Reviews number (MathSciNet)
MR2228189
Zentralblatt MATH identifier
1156.34021
Subjects
Primary: 34B10: Nonlocal and multipoint boundary value problems 39A10: Difference equations, additive
Keywords
Time scales oscillation Riccati equation telescoping principle
Citation
Erbe, Lynn; Kong, Lingju; Kong, Qingkai. A Telescoping Principle for Oscillation of Second Order Differential Equations on a Time Scale. Rocky Mountain J. Math. 36 (2006), no. 1, 149--181. doi:10.1216/rmjm/1181069493. https://projecteuclid.org/euclid.rmjm/1181069493
References
- R.P. Agarwal and M. Bohner, Basic calculus on time scales and some of its applications, Results Math. 35 (1999), 3-22.Mathematical Reviews (MathSciNet): MR1678096
- M. Bohner and A. Peterson, Dynamic equations on time scales, An introduction with applications, Birkhauser, Boston, 2001.Mathematical Reviews (MathSciNet): MR1843232
- G.J. Butler, L.H. Erbe and A.A. Mingarelli, Riccati techniques and variational principles in oscillation theory for linear systems, Trans. Amer. Math. Soc. 303 (1987), 263-282.Mathematical Reviews (MathSciNet): MR896022
Zentralblatt MATH: 0648.34031
Digital Object Identifier: doi:10.2307/2000793 - S. Chen and L.H. Erbe, Riccati techniques and discrete oscillations, J. Math. Anal. Appl. 142 (1989), 468-487.Mathematical Reviews (MathSciNet): MR1014591
Zentralblatt MATH: 0686.39001
Digital Object Identifier: doi:10.1016/0022-247X(89)90015-2 - --------, Oscillation and nonoscillation for systems of self-adjoint second order difference equation, SIAM J. Math. Anal. 20 (1989), 939-949.
- L.H. Erbe, Oscillation criteria for second order linear equations on a time scale, Canadian Appl. Math. Quart. 9 (2001), 345-375.
- L.H. Erbe and S. Hilger, Sturmian theory on measure chains, Differential Equations Dynam. Sys. 1 (1993), 223-246.Mathematical Reviews (MathSciNet): MR1258900
- P. Hartman, On linear second order differential equations with small coefficients, Amer. J. Math. 73 (1951), 955-962.Mathematical Reviews (MathSciNet): MR45896
Digital Object Identifier: doi:10.2307/2372126
JSTOR: links.jstor.org - --------, On an ordinary differential equation involving a convex function, Trans. Amer. Math. Soc. 146 (1969), 179-202.Mathematical Reviews (MathSciNet): MR276539
Zentralblatt MATH: 0196.10703
Digital Object Identifier: doi:10.2307/1995167
JSTOR: links.jstor.org - S. Hilger, Analysis on measure chains-A unified approach to continuous and discrete calculus, Results Math. 18 (1990), 18-56.Mathematical Reviews (MathSciNet): MR1066641
- J.W. Hooker, M.K. Kwong and W.T. Patula, Oscillatory second order linear difference equations and Riccati equations, SIAM J. Math. Anal. 18 (1987), 54-63.Mathematical Reviews (MathSciNet): MR871820
Zentralblatt MATH: 0619.39005
Digital Object Identifier: doi:10.1137/0518004 - J.W. Hooker and W.T. Patula, Riccati type transformations for second order linear difference equations, J. Math. Anal. Appl. 82 (1981), 451-162.Mathematical Reviews (MathSciNet): MR629769
Zentralblatt MATH: 0471.39007
Digital Object Identifier: doi:10.1016/0022-247X(81)90208-0 - Q. Kong, Interval criteria for Oscillation of second order linear ordinary differential equations, J. Math. Anal. Appl. 229 (1999), 258-270.Mathematical Reviews (MathSciNet): MR1664352
Zentralblatt MATH: 0924.34026
Digital Object Identifier: doi:10.1006/jmaa.1998.6159 - Q. Kong and A. Zettl, Interval oscillation conditions for difference equation, SIAM J. Math. Anal. 26 (1995), 1047-1060.Mathematical Reviews (MathSciNet): MR1338373
Zentralblatt MATH: 0828.39002
Digital Object Identifier: doi:10.1137/S0036141093251286 - M.K. Kwong and A. Zettl, Integral inequalities and second order linear oscillation, J. Differential Equations 45 (1982), 16-23.Mathematical Reviews (MathSciNet): MR662484
Zentralblatt MATH: 0498.34022
Digital Object Identifier: doi:10.1016/0022-0396(82)90052-3 - H.J. Li, Oscillation criteria for second order linear differential equations, J. Math. Anal. Appl. 194 (1995), 217-234.Mathematical Reviews (MathSciNet): MR1353077
Zentralblatt MATH: 0836.34033
Digital Object Identifier: doi:10.1006/jmaa.1995.1295 - C. Olech, Z. Opial and T. Wazewski, Sur le probleme d'oscillation des integrales de l'equation $y''+g(t)y=0$, Bull. Acad. Polon. Sci. 5 (1957), 621-626.Mathematical Reviews (MathSciNet): MR89312
- W.T. Patula, Growth and oscillation properties of second order linear difference equations, SIAM J. Math. Anal. 10 (1979), 55-61.Mathematical Reviews (MathSciNet): MR516749
Zentralblatt MATH: 0397.39001
Digital Object Identifier: doi:10.1137/0510006 - --------, Growth, oscillation and comparison theorems for second order linear difference equations, SIAM J. Math. Anal. 10 (1979), 1272-1279.Mathematical Reviews (MathSciNet): MR547812
Zentralblatt MATH: 0433.39005
Digital Object Identifier: doi:10.1137/0510114 - J.S.W. Wong, Oscillation and nonoscillation of solutions of second order linear differential equations with integral coefficients, Trans. Amer. Math. Soc. 144 (1969), 197-215.Mathematical Reviews (MathSciNet): MR251305
Zentralblatt MATH: 0195.37402
Digital Object Identifier: doi:10.2307/1995277
JSTOR: links.jstor.org - --------, Oscillation theorems for second order nonlinear differential equations, Bull. Inst. Math. Acad. Sinica 3 (1975), 283-309.
- You have access to this content.
- You have partial access to this content.
- You do not have access to this content.
More like this
- Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications
Zhu, Jiang and Liu, Dongmei, Abstract and Applied Analysis, 2013 - Generalized Variational Principles on Oscillation for Nonlinear Nonhomogeneous
Differential Equations
Shao, Jing and Meng, Fanwei, Abstract and Applied Analysis, 2011 - ON THE HOMOGENIZATION OF SECOND ORDER DIFFERENTIAL EQUATIONS
Jiang, Jiann-Sheng, Kuo, Kung-Hwang, and Lin, Chi-Kun, Taiwanese Journal of Mathematics, 2005
- Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications
Zhu, Jiang and Liu, Dongmei, Abstract and Applied Analysis, 2013 - Generalized Variational Principles on Oscillation for Nonlinear Nonhomogeneous
Differential Equations
Shao, Jing and Meng, Fanwei, Abstract and Applied Analysis, 2011 - ON THE HOMOGENIZATION OF SECOND ORDER DIFFERENTIAL EQUATIONS
Jiang, Jiann-Sheng, Kuo, Kung-Hwang, and Lin, Chi-Kun, Taiwanese Journal of Mathematics, 2005 - Oscillation and nonoscillation of certain second order quasilinear dynamic equations
Xu, Zhiting and Wang, Yuanfeng, Hiroshima Mathematical Journal, 2012 - On the Oscillation for Second-Order Half-Linear Neutral Delay Dynamic Equations on Time Scales
Zhang, Quanxin and Song, Xia, Abstract and Applied Analysis, 2014 - Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales
Lin, Quanwen, Jia, Baoguo, and Wang, Qiru, Abstract and Applied Analysis, 2010 - Interval Oscillation Criteria for Forced Second-Order Nonlinear Delay Dynamic Equations with Damping and Oscillatory Potential on Time Scales
Agwa, Hassan A., Khodier, Ahmed M. M., and Hassan, Heba A., International Journal of Differential Equations, 2016 - Oscillation Theorems for Second-Order Half-Linear Neutral Delay Dynamic Equations with Damping on Time Scales
Zhang, Quanxin and Liu, Shouhua, Abstract and Applied Analysis, 2013 - Oscillation Criteria for Second-Order Nonlinear Dynamic Equations on Time Scales
Zhang, Shao-Yan and Wang, Qi-Ru, Abstract and Applied Analysis, 2012 - Fite-Wintner-Leighton-Type Oscillation Criteria for Second-Order
Differential Equations with Nonlinear Damping
Pašić, Mervan, Abstract and Applied Analysis, 2013