Yeniçerioğlu, Ali Fuat The behavior of solutions of second order delay differential equations. (English) Zbl 1118.34074 J. Math. Anal. Appl. 332, No. 2, 1278-1290 (2007). Summary: We study the behavior of solutions of second-order delay differential equation \[ y''(t)=p_1y'(t)+p_2y'(t-\tau)+q_1y(t)+q_2y(t-\tau), \] where \(p_1,p_2,q_1,q_2\) are real numbers, \(\tau\) is positive real number. A basic theorem on the behavior of solutions is established. As a consequence of this theorem, a stability criterion is obtained. Cited in 18 Documents MSC: 34K25 Asymptotic theory of functional-differential equations 34K06 Linear functional-differential equations 34K20 Stability theory of functional-differential equations Keywords:characteristic equation; stability; trivial solution PDFBibTeX XMLCite \textit{A. F. Yeniçerioğlu}, J. Math. Anal. Appl. 332, No. 2, 1278--1290 (2007; Zbl 1118.34074) Full Text: DOI References: [1] Bellman, R.; Cooke, K., Differential-Difference Equations (1963), Academic Press: Academic Press New York [2] Cahlon, B.; Schmidt, D., Stability criteria for certain second-order delay differential equations with mixed coefficients, J. Comput. Appl. Math., 170, 79-102 (2004) · Zbl 1064.34060 [3] Driver, R. D., Exponential decay in some linear delay differential equations, Amer. Math. Monthly, 85, 9, 757-760 (1978) · Zbl 0417.34109 [4] Driver, R. D., Ordinary and Delay Differential Equations, Appl. Math. Sci., vol. 20 (1977), Springer: Springer Berlin · Zbl 0374.34001 [5] El’sgol’ts, L. E.; Norkin, S. B., Introduction to the Theory and Application of Differential Equations with Deviating Arguments (1973), Academic Press: Academic Press New York · Zbl 0287.34073 [6] Hale, J. K.; Verduyn Lunel, S. M., Introduction to Functional Differential Equations (1993), Springer: Springer Berlin · Zbl 0787.34002 [7] Hu, G. D.; Mitsui, T., Stability of numerical methods for system of neutral delay differential equations, BIT, 35, 505-515 (1995) [8] Kolmanovski, V.; Myshkis, A., Applied Theory of Functional Differential Equations (1992), Kluwer Academic: Kluwer Academic Dordrecht [9] Kordonis, I.-G. E.; Philos, Ch. G., The behavior of solutions of linear integro-differential equations with unbounded delay, Comput. Math. Appl., 38, 45-50 (1999) · Zbl 0939.45005 [10] Macdonald, N., Biological Delay Systems: Linear Stability Theory (1989), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0669.92001 [11] Philos, Ch. G.; Purnaras, I. K., Periodic first order linear neutral delay differential equations, Appl. Math. Comput., 117, 203-222 (2001) · Zbl 1029.34061 [12] Steele, C. R., Studies of the Ear, (Lectures in Appl. Math., vol. 17 (1979), Amer. Math. Soc.: Amer. Math. Soc. Providence, RI), 69-71 · Zbl 0424.92006 [13] Tobias, S. A., Machine Tool Vibrations (1965), Blackie: Blackie London [14] Yalçınbaş, S.; Yeniçerioğlu, F., Exact and approximate solutions of second order including function delay differential equations with variable coefficients, Appl. Math. Comput., 148, 287-298 (2004) · Zbl 1044.65063 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.