Oscillatory behavior of second order nonlinear differential equations with a sublinear neutral term
Abstract
The authors establish some new criteria for the oscillation of solutions of second order nonlinear differential equations with a sublinear neutral term by reducing the equation to a linear one. Their results are illustrated with an example.
Keyword : oscillation, second order, neutral differential equations, sublinear neutral term
How to Cite
Grace, S. R., & Graef, J. R. (2018). Oscillatory behavior of second order nonlinear differential equations with a sublinear neutral term. Mathematical Modelling and Analysis, 23(2), 217-226. https://doi.org/10.3846/mma.2018.014
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
[1] R.P. Agarwal, M. Bohner, T. Li and C. Zhang. Oscillation of second order differential equations with a sublinear neutral term. Carpathian J. Math., 30:1–6, 2014.
[2] L. Erbe, T. Hassan and A. Peterson. Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. J. Diff. Eqn. Appl., 15(11–12):1097–1116, 2009. https://doi.org/10.1080/10236190902785199
[3] L. Erbe, A. Peterson and P. Rehak. Comparison theorems for linear dynamic equations on time scales. J. Math. Anal. Appl., 275(1):418–438, 2002. https://doi.org/10.1016/S0022-247X(02)00390-6
[4] S.R. Grace, R.P. Agarwal, M. Bohner and D. O’Regan. Oscillation of second order strongly superlinear and strongly sublinear dynamic equations. Comum. Nonlinear Sci. Numer. Stimul., 14(8):3463–3471, 2009. https://doi.org/10.1016/j.cnsns.2009.01.003
[5] S.R. Grace, R.P. Agarwal, B. Kaymakalan and W. Sae-jie. Oscillation theorems for second order nonlinear dynamic equations. Appl. Math. Comput., 32(1):205–218, 2010. https://doi.org/10.1007/s12190-009-0244-7
[6] S.R. Grace, R.P. Agarwal and D. O’Regan. A selection of oscillation criteria for second order differential inclusions. Appl. Math. Letters, 22(2):153–158, 2009. https://doi.org/10.1016/j.aml.2008.01.006
[7] S.R. Grace, M. Bohner and R.P. Agarwal. On the oscillation of second order half-linear dynamic equations. J. Difference Eqn. Appl., 15(5):451–460, 2009. https://doi.org/10.1080/10236190802125371
[8] S.R. Grace, E. Akın and M. Dikmen. On the oscillation of second order nonlinear neutral dynamic equations with distributed deviating arguments on time scales. Dynam. Systems Appl., 23:735–748, 2014.
[9] G.H. Hardy, I.E. Littlewood and G. Polya. Inequalities. Cambridge University Press, 1959.
[10] C.G. Philos. On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays. Arch. Math. (Basel), 36(1):168–178, 1981. https://doi.org/10.1007/BF01223686
[2] L. Erbe, T. Hassan and A. Peterson. Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. J. Diff. Eqn. Appl., 15(11–12):1097–1116, 2009. https://doi.org/10.1080/10236190902785199
[3] L. Erbe, A. Peterson and P. Rehak. Comparison theorems for linear dynamic equations on time scales. J. Math. Anal. Appl., 275(1):418–438, 2002. https://doi.org/10.1016/S0022-247X(02)00390-6
[4] S.R. Grace, R.P. Agarwal, M. Bohner and D. O’Regan. Oscillation of second order strongly superlinear and strongly sublinear dynamic equations. Comum. Nonlinear Sci. Numer. Stimul., 14(8):3463–3471, 2009. https://doi.org/10.1016/j.cnsns.2009.01.003
[5] S.R. Grace, R.P. Agarwal, B. Kaymakalan and W. Sae-jie. Oscillation theorems for second order nonlinear dynamic equations. Appl. Math. Comput., 32(1):205–218, 2010. https://doi.org/10.1007/s12190-009-0244-7
[6] S.R. Grace, R.P. Agarwal and D. O’Regan. A selection of oscillation criteria for second order differential inclusions. Appl. Math. Letters, 22(2):153–158, 2009. https://doi.org/10.1016/j.aml.2008.01.006
[7] S.R. Grace, M. Bohner and R.P. Agarwal. On the oscillation of second order half-linear dynamic equations. J. Difference Eqn. Appl., 15(5):451–460, 2009. https://doi.org/10.1080/10236190802125371
[8] S.R. Grace, E. Akın and M. Dikmen. On the oscillation of second order nonlinear neutral dynamic equations with distributed deviating arguments on time scales. Dynam. Systems Appl., 23:735–748, 2014.
[9] G.H. Hardy, I.E. Littlewood and G. Polya. Inequalities. Cambridge University Press, 1959.
[10] C.G. Philos. On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays. Arch. Math. (Basel), 36(1):168–178, 1981. https://doi.org/10.1007/BF01223686