New oscillation criteria for forced superlinear neutral type differential equations
Downloads
DOI:
https://doi.org/10.26637/mjm0101/009Abstract
Some new oscillation criteria are established for the neutral type differential equation
(a(t)((x(t)+p(t)x(τ(t)))′)α)′+q(t)xβ(t)=e(t),t≥t0,
which are applicable to equations with nonnegative forcing term. Examples are provided to illustrate the results.
Keywords:
Neutral differential equation, second order, oscillation, superlinearMathematics Subject Classification:
34C15- Pages: 67-72
- Date Published: 01-09-2012
- Vol. 1 No. 1 (2012): Inaugural Issue :: Malaya Journal of Matematik (MJM)
R.P. Agarwal, S.R. Grace and D.O’Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic, Dordrecht, 2000. DOI: https://doi.org/10.1007/978-94-015-9401-1
L.H. Erbe, A. Peterson, T.S. Hasan and S.H. Saker, Interval oscillation criteria for forced second order nonlinear delay dynamic equations with oscillatory potential, Dyn. Cont. Disc. Syst. A, 17(2010), 533-542.
L. H. Erbe, Q. Kong and B. G. Zhang, Oscillation Theory For Functional Differential Equations, Marcel Dekker, New York, 1995.
L.H. Erbe, A. Peterson and S.H. Saker, Oscillation criteria for a forced second order nonlinear dynamic equations, J. Diff. Eqns. Appl., 14(2008), 997-1009. DOI: https://doi.org/10.1080/10236190802332175
A.G. Kartsatos, On the maintenance of oscillations of n th order equations under the effect of a small forcing term, J. Differ. Equ., 10(1971), 355-363. DOI: https://doi.org/10.1016/0022-0396(71)90058-1
A.G. Kartsatos, Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. Math. Soc., 33(1972), 377-383. DOI: https://doi.org/10.1090/S0002-9939-1972-0330622-0
Q. Kong and J.S.W. Wong, Oscillation of a forced second order differential equations with a deviating argument, Funct. Diff. Equ., 17(2010), 141-155.
Q. Kong and B.G. Zhang, Oscillation of a forced second order nonlinear equation, Chin. Ann. Math., 15B:1(1994), 59-68.
G.S. Ladde,V. Lakshmikantham and B.G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker, New York, 1987.
A.H. Nazar, Sufficient conditions for the oscillation of forced superlinear second order differential equations with oscillatory potential, Proc. Amer. Math. Soc., 126(1998), 123-125. DOI: https://doi.org/10.1090/S0002-9939-98-04354-8
Y.G. Sun and J.S.W. Wong, Forced oscillation of second order superlinear differential equations, Math. Nachr., 278(2005), 1621 -1628. DOI: https://doi.org/10.1002/mana.200410327
Y.G. Sun and J.S.W. Wong, Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J. Math. Anal. Appl., 334(2007), 549-560. DOI: https://doi.org/10.1016/j.jmaa.2006.07.109
J.S.W.Wong, Second order nonlinear forced oscillations, SIAM J. Math. Anal., 19(1998), 667-675. DOI: https://doi.org/10.1137/0519047
Q.G. Yang, Interval oscillation criteria for a forced second order nonlinear ordinary differential equation with oscillatory potential, Appl. Math., 136(2003), 49-64. DOI: https://doi.org/10.1016/S0096-3003(01)00307-1
- NA
Similar Articles
- Velusamy Kavitha, Peng-Zhen Wang, R. Murugesu , Existence results for neutral functional fractional differential equations with state dependent-delay , Malaya Journal of Matematik: Vol. 1 No. 1 (2012): Inaugural Issue :: Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2012 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
