Gizem S. Oztepe, Fatma Karakoc, Huseyin Bereketoglu (2017)
Communications in Mathematics
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This paper concerns with the existence of the solutions of a second order impulsive delay differential equation with a piecewise constant argument. Moreover, oscillation, nonoscillation and periodicity of the solutions are investigated.
Shao Yuan Huang, Sui Sun Cheng (2012)
Annales Polonici Mathematici
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Several recent oscillation criteria are obtained for nonlinear delay impulsive differential equations by relating them to linear delay impulsive differential equations or inequalities, and then comparison and oscillation criteria for the latter are applied. However, not all nonlinear delay impulsive differential equations can be directly related to linear delay impulsive differential equations or inequalities. Moreover, standard oscillation criteria for linear equations cannot be applied...
Dimitrova, M.B., Mishev, D. (2005)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Tripathy, A.K. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Li, Tongxing, Han, Zhenlai, Zhao, Ping, Sun, Shurong (2010)
Advances in Difference Equations [electronic only]
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Han, Zhenlai, Li, Tongxing, Sun, Shurong, Chen, Weisong (2010)
Advances in Difference Equations [electronic only]
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Bing Liu, Aimin Zhao, Jurang Yan (1997)
Collectanea Mathematica
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In this paper we study two classes of delay partial difference equations with constant coefficients. Explicit necessary and sufficient conditions for the oscillation of the solutions of these equations are obtained.
Yan, Weiping, Yan, Jurang (1996)
International Journal of Mathematics and Mathematical Sciences
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George E. Chatzarakis, Ponnuraj Dinakar, Srinivasan Selvarangam, Ethiraju Thandapani (2022)
Mathematica Bohemica
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We obtain some new sufficient conditions for the oscillation of the solutions of the second-order quasilinear difference equations with delay and advanced neutral terms. The results established in this paper are applicable to equations whose neutral coefficients are unbounded. Thus, the results obtained here are new and complement some known results reported in the literature. Examples are also given to illustrate the applicability and strength of the obtained conditions over the known...
Han, Zhenlai, Li, Tongxing, Zhang, Chenghui, Sun, Ying (2011)
Abstract and Applied Analysis
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Ireneusz Kubiaczyk, Samir H. Saker (2002)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear case. Some examples are considered to illustrate our main results.
B. Szmanda (1980)
Publications de l'Institut Mathématique
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Bozena Mihalíková (1999)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The aim of this paper is to present the sufficient conditions for oscillation of solutions of the system of differential equations of neutral type.