Tunç, Cemil; Biçer, Emel Stability to a kind of functional differential equations of second order with multiple delays by fixed points. (English) Zbl 1470.34204 Abstr. Appl. Anal. 2014, Article ID 413037, 9 p. (2014). Summary: We discuss the stability of solutions to a kind of scalar Liénard type equations with multiple variable delays by means of the fixed point technique under an exponentially weighted metric. By this work, we improve some related results from one delay to multiple variable delays. MSC: 34K20 Stability theory of functional-differential equations PDF BibTeX XML Cite \textit{C. Tunç} and \textit{E. Biçer}, Abstr. Appl. Anal. 2014, Article ID 413037, 9 p. (2014; Zbl 1470.34204) Full Text: DOI OpenURL References: [1] Burton, T. A., Stability by Fixed Point Theory for Functional Differential Equations, (2006), Mineola, NY, USA: Dover Publications, Mineola, NY, USA · Zbl 1160.34001 [2] Burton, T. A.; Furumochi, T., Fixed points and problems in stability theory for ordinary and functional differential equations, Dynamic Systems and Applications, 10, 1, 89-116, (2001) · Zbl 1021.34042 [3] Burton, T. A., Fixed points, stability, and exact linearization, Nonlinear Analysis: Theory, Methods & Applications, 61, 5, 857-870, (2005) · Zbl 1067.34077 [4] Pi, D., Study the stability of solutions of functional differential equations via fixed points, Nonlinear Analysis: Theory, Methods & Applications, 74, 2, 639-651, (2011) · Zbl 1248.34108 [5] Fan, M.; Xia, Z.; Zhu, H., Asymptotic stability of delay differential equations via fixed point theory and applications, Canadian Applied Mathematics Quarterly, 18, 4, 361-380, (2010) · Zbl 1237.34125 [6] Raffoul, Y. N., Stability in neutral nonlinear differential equations with functional delays using fixed-point theory, Mathematical and Computer Modelling, 40, 7-8, 691-700, (2004) · Zbl 1083.34536 [7] Jin, C.; Luo, J., Fixed points and stability in neutral differential equations with variable delays, Proceedings of the American Mathematical Society, 136, 3, 909-918, (2008) · Zbl 1136.34059 [8] Zhang, R.; Liu, G., Stability of nonlinear neutral differential equation via fixed point, Annals of Differential Equations, 28, 4, 488-493, (2012) · Zbl 1274.34220 [9] Ardjouni, A.; Djoudi, A., Fixed points and stability in nonlinear neutral Volterra integro-differential equations with variable delays, Electronic Journal of Qualitative Theory of Differential Equations, 20–37, 1-13, (2013) · Zbl 1340.34286 [10] Tunç, C., New stability and boundedness results of Liénard type equations with multiple deviating arguments, Journal of Contemporary Mathematical Analysis, 45, 4, 47-56, (2010) · Zbl 1302.34108 [11] Tunç, C., Stability, boundedness and uniform boundedness of solutions of nonlinear delay differential equations, Discrete and Continuous Dynamical Systems A, 1395-1403, (2011) · Zbl 1306.34114 [12] Tunç, C., Stability and boundedness in multi delay Lienard equation, Filomat, 27, 3, 437-447, (2013) [13] Tunç, C., Stability to vector Liénard equation with constant deviating argument, Nonlinear Dynamics, 73, 3, 1245-1251, (2013) · Zbl 1281.34102 [14] Tunç, C., A note on the bounded solutions to \(x^{\operatorname{\prime\prime}} + c(t, x, x^\prime) + q(t) b(x) = f(t)\), Applied Mathematics & Information Sciences, 8, 1, 393-399, (2014) [15] Tunç, C.; Yazgan, R., Existence of periodic solutions to multidelay functional differential equations of second order, Abstract and Applied Analysis, 2013, (2013) [16] Tunç, C., New results on the existence of periodic solutions for Rayleigh equation with state-dependent delay, Journal of Mathematical & Fundamental Sciences, 45, 2, 154-162, (2013) 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.